# Sound - DOC

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```					                                                   Sound
Vs (air 20.oC = 343 m/s; air 0oC = 331 m/s; He 1005 m/s; water = 1440 m/s; aluminum 5100 m/s
Origin of Sound: pg. 380-382
1. Sounds are produced by ____________ of material objects. The vibration sends a disturbance through
the surrounding medium in the form of a ______________ waveform.
2. Under ordinary conditions the frequency of the source is ____________ to the frequency of the sound
waves produced.
3. Sound in air is consisted of a series of compressions and rarefactions (compressions are regions of
_______ pressure, rarefactions are regions of ______ pressure).
4. Sound requires a _________ (it is a _____________ wave). As in all mechanical wave motion, it’s
not the medium that travels from one point to another, the wave ______.
5. Sound travels faster in ___________ than in ___________ than in gases. The speed of sound depends
not on the materials density but on its _____________.
6. In air, the speed of sound varies with ____________. The velocity increases ___ m/s for every 1º C.
At 0º C, sound travels ___________ m/s.
Vs = (331.0 + 0.60 (T)) m/s T = ºC

Pitch, infrasonic and ultrasonic:
1. Pitch is the ear’s perception of _______________. A high pitch is the result of a _______ frequency, a
low pitch is from a ______ frequency.
2. The human ear can perceive a frequency range from __ to ________ Hz.
3. Sound waves below 20 Hz are called _____________ sounds. Natural sources of infrasonic sound
include earthquakes, thunder and volcanoes.
4. Sound waves above 20,000 Hz are called ____________. Dogs can hear frequencies as high as
50,000 Hz and bats can hear up to 100,000 Hz. Ultrasonic sound gives parents a chance to look at their
________ in the womb. See fig. to the right.

Loudness: pg. 398-400
1. Loudness is a person’s perception of the ______________(A) of a sound wave. Sound waves are
regions of high pressure ( _____________) and low pressure (_______________). Amplitude measures
the fluctuations of _____________ from equilibrium within the medium. Pressure fluctuations for
normal conversation are about ___ Pa compared to standard atmospheric pressure which is
_________ kPa. (your ears are very sensitive).
See figure below:

2. Loudness is a ____________ property because everyone has their own perception of loudness.
Amplitude is an objective property that can be ___________ with a device called an oscilloscope (pg.
382and 398).
3. Loudness is described by a measure of the ____________ (I). Intensity varies with the _______ of the
amplitude of a sound wave (double the amplitude will increase the intensity by a factor of ___).
4. Sound waves carry _________ that can be used to perform work, such as an eardrum to vibrate.
Sound intensity (I) is the __________ (P = work/time) that passes perpendicularly through some ______
(A).
I = P/A (units are W/m2).

5. The intensity _____________ with the square of the distance from the source. If the distance from the
source triples the sound will decrease __ times.
I = P/4 πr2 (r is the distance from the source)
I1r12 = I2r22
6a. Sound levels are used to quantify loudness through what is called a _________ (dB) scale. Here, the
intensity from some source is compared to the lowest perceivable intensity called the __________ of
hearing (Io = 1.00 . 10-12 W/m2).
b. This decibel scale is a logrithmetic scale defined by the following:
β = 10 log (I/ Io)
β is the Intensity level and is measure in decibels

Sources                 Intensity Level (dB)            Intensity (W/m2)
threshold of hearing            0                        1.00 . 10-12
normal breathing                 10.00                   1.00 . 10-11
close whisper                    20.00                   1.00 . 10-10
baby’s coo                       30.00                   1.00 . 10-9
quiet radio                      40.00                   1.00 . 10-8  (pg. 400 for more)

c. Every increase by 10 dB corresponds to an increase in loudness by a factor of 2. An increase of 20 dB
corresponds to an increase in loudness by a factor of ___. An increase of 30 dB corresponds to an
increase in loudness by a factor of ___.
d. Every increase of 10 dB corresponds to an increase in intensity by a factor of 10. An increase of 20
dB corresponds to an increase in intensity of _____. An increase of 30 dB corresponds to an increase in
intensity by a factor of ____.
e. For intensity levels (dB) only digits from the one’s place and to the ________ of the one’s place are
significant.

Homework:
1. What are all sources of sound?
2. How does pitch relate to frequency?
3. What is the average frequency range of a young person’s hearing?
4. Distinguish between infrasonic and ultrasonic sound.
5. a. Distinguish between compressions and rarefactions of a sound wave.
b. How are compressions and rarefactions produced?
6. Light can travel through a vacuum, as is evidenced when you see the sun or the moon. Can sound
travel through a vacuum also? Explain why or why not.
7. a. How fast does sound travel in dry air at room temperature?
b. How does air temperature affect the speed of sound?
8. How does the speed of sound in air compare with its speed in water and in steel?
9. Why does sound travel faster in solids and liquids than in gases?
10. Why is sound louder when a vibrating source is held to a sounding board?
11. When watching a baseball game, we often hear the bat hitting the ball after we actually see the hit.
Why?
12. Why will marcher at the end of a long parade following a band be out of step with marchers nearer
the band?
13. You watch a distant farmer driving a stake into the ground with a sledgehammer. He hits the stake at
a regular rate of one stroke per second. You hear the sound of the blows exactly synchronized with
the blows you see. And then you hear one more blow after you see him stop hammering. How far
away is the farmer?
Some Pretty Sound Advice: Do Your Homework
Sample Problems:
1. 1.2.10-4 W of power passes perpendicularly through two surface areas. Area 1 is 4.0 m2 and Area 2 is 12 m2.
a. Determine the sound intensity at each area.

b. Determine the distance to each area from the source.

2. During a fireworks display, a rocket explodes high in the air. The sound of the blast reaches listener 2 (who is
640. m from the blast) with an intensity of 0.10 W/m2. Determine the intensity of the sound that reaches a
person standing 160. m from the blast.

3. What is the intensity level of a sound wave whose intensity is 2.0 W/m2?

4. What is the intensity of a sound wave with an intensity level of 73.0 dB?

Homework:
1. An intensity level increases by 40. dB.
a. By what factor does perceived loudness increase?
b. By what factor does wave intensity increase?
2. An intensity increases by a factor of 1000.
a. By what factor does intensity level increase?
b. By what factor does perceived loudness increase?
3. What is the speed of sound at 25oC.
4. At what temperature will sound travel 336 m/s?
5. Is loudness an objective or subjective property? Why?
6. How does sound intensity vary with distance from the source?
7. The Intensity of an explosion is 1.00.109 W/m2 at a distance of 100. m from the explosion. What will be the
intensity of the explosion from a distance of 1.50 km from the explosion?
8. The sound intensity from an explosion if 1.6 .104 W/m2 when located 5.0 km from the source. From what distance
from the explosion will the intensity be 120 W/m2?
9. When a sound registers an intensity level of 94.0 dB, what is the intensity?
10. When a sound intensity registers 1.36.10-6 W/m2, what will be the intensity level?
11. What two physics mistakes occur in a science fiction movie when you see and hear at the same time a distant
explosion in outer space?
12. When a sound wave propagates past a point in the air, what are the changes that occur in the pressure of air at
this point?
13. How much more intense is (a) a close whisper than the threshold of hearing? (b) a close whisper than normal
breathing?
14. The signal-to-noise ration of a tape recorder is listed at 50dB, meaning that when music is played back, the
intensity level of the music is 50 dB grater than that of the noise from tape hiss and so forth. By what factor is the
sound intensity of the music greater than that of the noise?
Intensity of Sound

{
A. Loudness vs. Intensity (Perception vs. Reality)                          β       Intensity level in decibels
.    -12 W   2
B. Intensity ( I = P/A ) vs. Intensity level (β)                              Io    threshold of hearing (1.00 10      /m )
. -12 W 2
1. Threshold of Hearing (Io = 1.00 10         /m )
I      intensity of sound being measured
2. Intensity Level Scale                  decibels
3. β = 10 log (I/Io)
Solving Intensity Level Problems
Example 1:
If a cannon is measured to have an intensity level of 120. dB by a meter from a certain distance, what will be the
intensity level of 3 identical cannons (the waves that are produced from each cannon are identical) firing from the
same location? You may think that since there are three, the intensity level would be ______ dB. But this is not
correct because Intensity Levels (β) are not additive, but sound ____________ (I) are additive.

Example 2: If 3 identical radios create a measured intensity level of 110. dB when measured from a certain
distance. What would be the intensity level of 1 radio when perceived from the same distance?

Example 3: If 4 car horns creates an intensity level of 95 dB, what would be the intensity level of 9 car horns when
measured from the same distance?

Example 4: What would be the resulting intensity level if one tiger made a growl of 55dB and another tiger growled
at 58 dB and were heard from the same distance?

Homework:
1. A radio is playing with an intensity level of 40. dB. What would be the intensity level of 4 such radios playing
together?
2. If 5 identical cannons create an intensity level of 150.dB when fired simultaneously, what would be the intensity
level of just one of these cannons being fired?
3. At a certain distance away, a thermonuclear explosion has an intensity level of 177 dB. What would be the
intensity level of 6 such explosions?
4. A 21 gun salute has an intensity level of 100.dB. What would be the intensity level of a 6 gun salute?
5. What would be the resulting intensity level if an 80.db, 85 db, and a 93 db sound were heard simultaneously?
Some Intense Problems (how does that sound? Hopefully they match your level)
Example #1: A bee’s wings emit an intensity level of 45.0 dB from a distance of 10. m. What would be
the intensity level from 1.0 m?

Example #2: 50 mosquitoes emit an intensity level of 58.0 dB from 8.0 m. What would be the intensity
level of 220 mosquitoes from 3.0 m.

Example #3: A dog’s bark has an intensity level of 80.0 dB from 5.0 m. Your next door neighbor 25.0 m
from you has 1 dog. Your neighbor across the street has 3 dogs and is 100.0 m from you. When all the
dogs bark, what intensity level will you hear?

Homework:
1. When Mr. Wilkins breaks a board from his Karate chop, 1 class of his students lets out a shrill scream
of horror that is perceived as 130.0 dB from a distance of 1.0 m. What would be the intensity level of 4
identical Wilkins classes when heard from 100. m?

2. 5 Cheerleaders yelling at the top of their lungs emits an intensity level of 62 dB when perceived by
people in the front row 10.0 m away. What would be the perceived intensity level of a squad of 20
cheerleaders by fans seated in the back of the stands 45.0 m away?

3. Mr. Mellott accidentally stepped on his cat’s tail which emitted an intensity level of 110. dB when
perceived from 5.00 m. Mr. Mellott’s accidental steppage on Mr. Wilkins’ dog’s tail results in the dog
emitting an intensity level of 106 dB when perceived from 3.00 m. What will be the resulting intensity
level of Mr. Mellott stepping on both the cat’s and dog’s tail when heard from 55.0 m?
Sound III
Ears Perception of Loudness: (Fletcher-Munson curves)
1. The perception of loudness (intensity________) by the human ear varies at different frequencies. (See the
chart below) Notice that the x-axis (frequency) has a range of ___ to _______ hz, this is the audible range.
2. Looking at the chart, observe how the perceived intensity level (___) is the same as the actual intensity
level from approximately _____ to _____ Hz.

3. At frequencies lower than 600Hz, the perceived intensity level_____ as the _______ decreases. Note that
the perceived intensity level at a frequency of 80 Hz is ____ dB for an actual intensity level of 50dB and that the
perceived intensity level at 100Hz is about 40 dB for an actual intensity level of ____ dB.

4. At frequencies higher than 4000 Hz, the perceived intensity level ___________as the frequency increases.
Note that the perceived intensity level at a frequency of 10,000 Hz is ____ dB for an actual intensity level of 30
dB and the perceived intensity level is 40 dB for an actual intensity level of ____ dB.

5. The ear is the most sensitive at a frequency of approximately ______ Hz. Here, a perceived intensity level
of 20 dB is actually _____ dB.

6. Notice, how the curves flattens at higher intensity levels. This indicates that as the intensity level increases,
the ear starts to become ______ sensitive to all frequencies. This is why when your stereo is _____ you can hear
all frequencies fairly well, but when you turn it down the ____ and ____ frequencies cut out. Many manufactures
of stereos include a ___________ button (or megabass) to compensate for the ear’s change is perceived intensity
levels at different _____.
Sound Quality
1. When musical instruments strike the same ____, your ear can easily discern a difference between each
instrument. This perceived difference is referred to as timbre.
2. To see how this works lets relate timbre to our knowledge of _____ waves.
a. Recall from standing waves in strings, that different numbers loops corresponded to different
______________ (or overtones). The first harmonic was referred to as the _____________.
b. The second harmonic is referred to as the ____ overtone and occurs at a frequency twice the
fundamental frequency (f2 = 2 fo) .
c. Doubling the frequency of a sound wave raise the pitch one ___________.
d. The ___ harmonic is referred to as the third overtone and occurs at a frequency _____ the
fundamental frequency. The pitch of the sound here is ____ octaves higher than the fundamental.
e. When a string is plucked in order to produce a sound, not only the fundamental but the _______
modes of vibration may be present. Fig. 21.4 pg. 401
f. The presence of multiple harmonics makes for a richer sound. The greater the numbers of
harmonics present the better the sound quality (________). When stringed instruments are played
they are close to one end to enhance the production of multiple __________. (See figure 21.5 pg.
401 and 21.10 pg. 404 and figure above) Note that the different harmonic frequencies also have
different amplitudes for different instruments playing the same note.
http://hypertextbook.com/physics/waves/music/

Sound Waves and Music:
1. We learned earlier that pitch is dependent upon the frequency of a sound wave and that the timbre (tone
quality) is dependent upon the number and amplitude of ________________ present in a sound wave.
2. We further saw that to have an increase of 1 octave one must ____ the frequency of the sound wave.
In music how is it determined what frequencies combine to form a major ____? The answer is the ratio of
frequencies must be _____. Example (look at the table): a ____ chord is comprised of the notes C (262Hz), E
(330 Hz), G (392 Hz) and C (524 Hz an _____ higher than the 262 Hz). If you divideC 1 by ___, E by ___, G by
___, and C2 by ____, that will correspond to a frequency of _____ Hz.

Questions:
1.   At approximately what frequency does the normal ear have a perceived intensity level equal to the actual
intensity level at any intensity level?
2.   At what frequency does the normal ear perceive intensity levels greater than the actual intensity level at any
intensity level?
3.       a. What is the ear’s perception of intensity level at 80 Hz. when the actual
intensity level is 40 dB?
b. What is the actual intensity level when the ear perceives an intensity level of 0 dB at 40 Hz.
c. What is the ear’s perception of intensity level when the actual intensity level is 100 dB at 80 Hz?
d. What is the ear’s perception of intensity level when actual intensity level is 100 dB at 40 Hz?
e. What can you conclude about how volume affects perceived intensity levels at different
frequencies?
4.   What is the purpose of a loudness button on stereos?
5.   What determines the sound quality (timbre) of a musical instrument?
6.   a. How does the frequency of the 4th harmonic compare to the fundamental?
b. How many octaves higher is the fourth harmonic that the fundamental?
7.   What is different about an A3 from a human alto and a piano?
8.   What is the ratio of frequencies that comprise a musical chord?
Sounds in Pipes and Strings
Pipes open at both ends                                  Pipes closed at one end
fn = nV/2L                    fn = nfo                    fn = nV/4L
λn = 2L / n                   v = λnfn                    λn = 4L / n
(n=1,2,3,4 . . . )                                        (n = 1,3,5,7 . . .)

fundamental

1st harmonic                                              1st harmonic

1st overtone

2nd harmonic                                              3rd harmonic

2nd overtone

3rd harmonic                                              5th harmonic

3rd overtone

4th harmonic                                             7th harmonic

4th overtone

5th harmonic                                              9th harmonic

There are many ways to create standing waves in the air. Woodwinds rely on vibrating reeds, brasses rely on
vibrations of a players lips, a flute is driven by a jet of air. There are 2 types of pipes to consider for creating
standing waves: open at both ends or closes at one end.
Examples:
#1: When all the holes of a standard flute are closed, the lowest note it can hit is middle C whose fundamental
frequency is 262 hz.
a. At 20.oC what is the length from the                    b. The flautist can alter the length of the flute by adjusting
mouthpiece to the end of the tube?                             the length to which the head is inserted into the main stem
(assume the tube to be open at both ends)                      of the instrument. If the air temperature rises to 32 oC, to
what length should the flute be adjusted?

c. What is the wavelength for the standing waves produced in parts a and b?

Example #2: In a Physics lab Rex and Peyton find that they can take a long glass tube and fill it with water and
create a standing wave by striking a tuning fork over the mouth of the tube. If the tuning fork has a fundamental
frequency of 440. hz and the room is 20.oC, how long is the air column that vibrates at the same frequency as the the
air column?
Sound Waves in Strings
Law of Lengths: The frequency of vibration and length         Law of Tensions: The frequency of vibration and
of a string are ________________ proportional.               tension impressed upon a string are __________
proportional to the square root of the tension on the string.

f1L1 = f2L2                                             f1 / F11/2 = f2 / F21/2

Law of Diameters: the frequency of vibration and             Law of Densities: the frequency of vibration and
diameter of a string are ___________________                 density of a string are______________ proportional to
proportional.                                                the square root of the density of the string.

f1d1 = f2d2                                             f1 D11/2 = f2 D21/2

Examples:
A string 3.00 m long has a tension of 25 N impressed upon it vibrates at 150. hz:
a. What will be the frequency of vibration if the    b. What will be the frequency of vibration if the length
tension is increased to 50. N?                       is changed to 2.20 m and the tension is increased to 75 N?

Homework:
1. A string 1.50 m long has a fundamental frequency of 340. hz. What is its fundamental frequency if it is
shortened to 1.20 m?

2.   A 36 cm string vibrates with a frequency with a frequency of 1250. hz. At what length will its frequency be
1500. hz?

3.   A string experiencing a tension of 25.0 N has a frequency of 260. hz. What is the new frequency if the tension
is decreased to 16.0 N?

4.   If a 480. hz string has a tension of 4.0 N on it, what must be the tension if the frequency is increased to
1920. hz?

5.   A 2.0 m string vibrates at 450 hz under a tension of 16 N. If the tension is increased to 25 N and the length is
shortened to 1.50 m, what is the new frequency?

6.   a. A pipe open at both ends is 2.0 m long. What is the frequency of the third overtone at 25 oC?
vs = (331.0 + .60(T))m/s T is measured in oC

b. What is the wavelength of the second harmonic?

7.   An air tube is 1.5 m long and closed at one end. What is the frequency of the fifth overtone at 10. oC?

8. What is the frequency of the third harmonic for a 1.0 m long tube open at both ends at 25 oC?
(use vs from problem 6)

9. What is the frequency of the third overtone of a 1.20 m long tube that is closed at one end at 10. oC?
(use vs from problem 7)

10. Joanna the church organist is practicing on her organ and determines that the first 2 overtones for the 370 hz
pipe occur at 1110 hz and 1850 hz. Is the pipe open at both ends or closed at one end? (Determine n from f n/fo
for the first and second overtones to see harmonic values)
Some Intense, Level, Sound Advice, Study Your Note Sheets for Your Sound Exam
Beats: (pg. 391-393)
1. Beats are an interference pattern formed when two sound waves of nearly equal ___________ are
superimposed. The result is a waveform that increases and decreases in ______________ (due to alternating
regions of constructive and destructive interference).
2. The beat frequency is the absolute value of the ________________ between the 2 frequencies. The time
between beats (one rise and fall) is the __________ of the beat (the inverse of the beat frequency).
Example: Tuning forks of frequency 440. and 442 Hz are struck together.
a. What is the beat frequency?            b. What is the period between beats?

Doppler Effect: (pg. 372-376)
1. Doppler Effect is a change in the apparent frequency of sound (pitch) due the __________ of the source or
the observer (Doppler effect can occur for any type of wave). (fig. 19.15-19.17 pg. 372-373)
2. When a high speed car passes you it has a ________ pitch as it approaches you and has a _________ pitch
as it moves away from you.
f = fo (v + vo)/(v – vs)
f = perceived frequency; fo = actual frequency
v = speed of sound vo = speed of observer vs = speed of source
vo is (+) when the observer moves _________ the source (- when moving ________ from source).
vs is (+) when the source moves __________ the observer (- when moving _________ from observer).

Example 1: Sitting on the beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of the
airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a
frequency of 1000. Hz, flies toward her at a speed of 100.0 m/s?

Example 2: In the previous example, what frequency will Sunny observe as the jet travels away from her at the
same speed?

Bow Waves (pg. 373)
1. A bow wave is a type of wave formed when the source of wave production (like a boat in the water) travels
_____________ than the waves themselves travel with the medium. The resulting 2-dimensional wave is a result of
_______________ interference of edges of overlapping waves (circles, as seen behind boats traveling faster than the
waves the it creates will travel through the water). (see fig. 19.18-19.20 pg. 373-374).
2. When the source travels at the same speed as the medium a wave _____________ forms in front of the source.
With more energy or thrust, the source may pass through the barrier, (for sound this is called breaking the
__________ barrier) and a bow wave forms behind the source.
3. Note the _________ the speed of the source, the more narrow the bow wave.

Shock Waves (pg. 374-376)
1. For aircraft, the bow wave is 3 dimensional ___________ dragging behind the aircraft (called a shock wave).
2. This shock wave _____________ continuously behind the plane and is heard by an observer once the shock wave
passes by them. See fig. 19.25 pg .375
3. The aircraft need not make a ___________ to create a shock wave, merely travel ___________ than the speed of
sound (bullets and whips make sonic booms).
4. Speeds faster than the speed of sound are called ______________ speeds.
5. The intensity of the shock wave ____________ with distance.
6. Mach number-comparison of speed of supersonic aircraft to speed of sound.
Mach number = vobject / vsound
Example: In the cold upper atmosphere, sound travels 300. m/s, if a supersonic aircraft travels 750 m/s in the upper
atmosphere, what is the mach number?
Another method of determining Mach number is through a comparison of distance the sound travels, the distance the
aircraft travels and the angle formed between the bow wave.
o
sin θ = vsound / vobject             θ = 90
mach # = 1/ sin θ                                         θ

Questions: (Day #1 evens; Day #2: odds)
1. When a source moves toward a receiver, does the receiver encounter an increase in wave frequency, wave speed
or both?
2. Does the Doppler effect occur for only some types of waves or all waves?
3. How fast must a bug swim to keep up with the waves it is producing? How fast must a boat move to produce a
bow wave?
4. Distinguish between a bow wave and a shock wave.
5. How fast must an aircraft fly in order to produce a sonic boom?
6. If you encounter a sonic boom is that evidence that an aircraft exceeded the speed of sound at the instant you
encounter the sonic boom?
7. How does the interference of sound relate to beats?
8. What is the beat frequency produced from a 494 hz tuning fork played with a 496 hz tuning fork?
9. Could the Doppler effect be called the apparent change in the speed of a wave due to the motion of the source?
10. Whenever you watch a high flying aircraft sound appears to be coming from behind the craft. Why is this so?
11. What happens to the conical angle of a supersonic aircraft as it gains speed?
12. Why is it that a subsonic aircraft cannot make a sonic boom no matter how loud it is?
o
13. What are the possible beat frequencies for tuning forks of 260. , 262 and 266 hz?          θ = 90
θ = 25o
Problems: (Day #1 evens; Day #2: odds)
Exercise 1:    If an airplane travels 463 m/s at 18 °C, what is its mach number?

Exercise 2:      Predict the mach number from the figure (right).

Exercise 3:      One foggy morning (T = 20.0oC), Kenny is driving his speed boat toward the Brant Point
lighthouse at a speed of 15.0 m/s as the fog horn blows with a frequency of 180.0 Hz. What
frequency does Kenny hear as he moves?

Exercise 4:      Dad is driving the family station wagon to Grandma’s house when he gets tired and pulls over in a
roadside rest stop to take a nap. Junior, who is sitting in the back seat, watches the trucks go by on
the highway and notices that they make a different sound when they are coming toward him than
they do when they are moving away. (T = 20.0 oC)
a) If a truck with a frequency of 85.0 Hz is traveling toward Junior with a speed of 27.0 m/s, what
frequency does Junior hear as the truck approaches?
b) After the truck passes, what frequency does Junior hear as the truck moves away?

Exercise 5:      One way to tell if a mosquito is about to sting is to listen for the Doppler shift as the mosquito is
flying. The buzzing sound of a mosquito’s wings is emitted at a frequency of 1050 Hz. (T=20.0 oC)
a) If you hear a frequency of 1034 Hz., does this mean that the mosquito is coming in for a landing
or that it has just bitten you and is flying away?
b) At what velocity is the mosquito flying?

Exercise 6:      Barney a bumblebee flying at 6.00 m/s, is being chased by Betsy, a bumblebee who is flying at
4.00 m/s. Barney’s wings beat with a frequency of 90.0 Hz. What frequency does Betsy hear as
she flies after Barney? (T=20.0 oC)

Exercise 7:      Mrs. Gonzalez is about to give birth and Mr. Gonzalez is rushing her to the hospital at a speed of
30.0 m/s. Witnessing the speeding car, Officer O’Malley jumps in his police car and turns on the
siren. While the officer chases after the Gonzalez’ car with a speed of 35.0 m/s, the frequency
perceived by the Gonzalez’ is 800. hz. What is the actual frequency of the siren? (T=20.0 oC)
Resonance Lab                                                Name ___________________________________

Objective: To determine the frequency of 4 tuning forks by the determination of the length of the column of air
which the tuning forks cause to resonate.

The wavelength of a standing wave of air in a pipe that is closed at one end is equal to 4L/n (where there are only
odd numbers of harmonics, we will use the first harmonic (fo) so n = 1).
The frequency is the ratio of the speed of sound and the wavelength as follows:     v = fn λn
Therefore, v = fn (4L/n) or          fn = nV           fo = V
4L               4L

The speed of sound is dependant on the temperature of the air as follows:          T: ________ oC (1 decimal place)
v = (331.0 + 0.60 T) m/s speed of sound (show calculation)
___________ m/s

Determine the length of the resonating columns of air in each tube below:

L1 (____) = ________ m L2 (____) = _________ m L3 (____) = _________ m                      L4 (____) = ________ m

Calculate the following (be sure to carry at least 1 extra significant digit when using a previously calculated value, but
do not report any extra significant digits in your final answer)

Frequency of Tuning Fork #1:        ____________       hz       Frequency of Tuning Fork #2: ___________ hz

Frequency of Tuning Fork #3:        ____________       hz       Frequency of Tuning Fork #4: ____________ hz

Theoretical Frequency of Tuning Fork:

#1 ____________ hz           #2 ____________ hz             #3 ____________ hz         #4 ____________ hz

% Error: be sure to carry at least 1 extra significant digit when using a previously calculated value

#1_______                       #2 ________            #3__________                   #4 _________
The Sound of a Review Sheet is Music to my Ears

1. How far will sound travel in 3.50 seconds in air at a temperature of 45.0oC?

2. If a sound has an intensity of 1.0 . 10-4 W/m2 from a distance of 10. km, at what distance will the
intensity be 3.5 . 10-5 W/m2?

3. When an intensity level is increased by 40. dB, how much greater will be the:
a. perceived loudness                b. the wave intensity

4. If 2 cannons create an intensity level of 115 dB, what will be the intensity level of 5 identical cannons
being fired from the same distance?

5. If an intensity level of 63 dB is heard simultaneously with an intensity level of 65 dB, determine the
resulting intensity level.

6. a. Determine the frequency of the second overtone of a 2.40 m long open pipe at 22oC.
b. Determine the wavelength of the second overtone of the pipe.

7. a. Determine the frequency of the second overtone of a 2.50 m long pipe that is closed at one end at
22oC.
b. Determine the wavelength of the second overtone of the pipe.

8. A 2.50 m long string has a fundamental frequency of 275 hz when a tension of 25.0 N is applied to it.
Determine the fundamental frequency of this string when the length of the string is shortened to 1.50
m and the tension decreased to 15.0 N.

9. An automobile travels 40.0 m/s while approaching a factory whistle that emits a frequency of 5000.0
hz. At 23oC, determine the frequency that the driver will perceive.

10. 2 tuning forks are struck together. One vibrates at a frequency of 412 hz while the other vibrates at a
frequency of 416 hz.
a. How many beats are heard each second?
b. How much time will there be between beats?

Equations:
vs = (331.0 + 0.60(oC))m/s = d/t          I1r12 = I2r22      I = P/A       β=10 log (I/I0)
(open pipes)     fn = nv/2L       λn = 2L/n         v = λnfn
(closed pipes) fn = nv/4L         λn = 4L/n                     _     __
f1L1=f2L2        f1/√F1=f2/√F2            f1d1=f2d2          f1√D1=f2√D2
fbeat=|f1-f2|    f=fo(v+vo)/(v-vs)

(doppler)
http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm

(cool doppler)
http://www.astro.ubc.ca/~scharein/a311/Sim.html#Doppler

(each case doppler)
http://www.kettering.edu/~drussell/Demos/doppler/doppler.html

(beats)
http://library.thinkquest.org/19537/java/Beats.html

(timbre)
http://ptolemy.eecs.berkeley.edu/eecs20/week8/
Sound Review Sheet Answers

1. v = (331.0 + 0.60 (T)) m/s
v = (331.0 + 0.60 (45.0)) m/s
v = (331.0 + 27.0) m/s = 358.0 m/s

v = d/t
d = vt
d = (358.0 m/s) (3.50 s)
d = 1250 m

2. I1 r12 = I2 r22
_______
r2 = √I1r12 / I2
___________________________________
r2 = √(1.0.10-4 W/m2)(10..103 m)2 / (3.5.10-5 W/m2)
r2 = 1.7.104 m = 17 km

3a. 24 or 16 times louder
b. 104 or 10,000 times the wave intensity

4. ß2 = 10 log (I2 /I0)                              I 5 = 5 (I2 / 2)
β/10
I = 10          Io                                   I5 = 5(0. 316 W/m2) / 2
I = 10 115/10 (1.00.10-12 W/m2)                      I5 = 0.791 W/m2
2
I2 = 0.316 W/m                                       ß5 = 10 log (I5 /I0)
ß5 = 10 log (0.791 W/m2 / 1.00.10-12W/m2)
ß5= 119 db

5. ß = 10 log (I /I0)                                ß’ = 10 log (I’ /I0)
I = 10 β/10 Io                                       I = 10 β/10 Io
I = 1063/10 (1.00.10-12W/m2)                         I = 1053/10 (1.00.10-12W/m2)
I = 1.995.10-6 W/m2                                  I’ = 3.16.10-6 W/m2

ITOT = I + I’                                        ßTOT = 10 log (ITOT / I0)
ITOT = 1.995.10-6 W/m2 + 3.16.10-6 W/m2              ßTOT = 10 log (5.16.10-6 W/m2 / 1.00.10-12W/m2)
Itot = 5.16.10-6 W/m2                                ßTOT = 67 db

6a. v = (331.0 + 0.60 (T)) m/s
v = (331.0 + 0.60 (22)) m/s
v = (331.0 + 13.2) m/s = 344.2 m/s

fn = nv/2L
f3 = 3 ( 344.2 m/s) / ((2)(2.40 m))
f3 = 215 hz

b. λ 3 = 2L / n
λ 3 = 2 (2.40 m ) / 3
λ 3 = 1.60 m

7a. v = (331.0 + 0.60 (T)) m/s        fn = nv/4L
v = (331.0 + 0.60 (22)) m/s       f5 = 5 ( 344.2 m/s) / ((4)(2.50 m))
v = (331.0 + 13.2) m/s            f5 = 172 hz
v = 344.2 m/s
7b. λ 5 = 4L / 5
λ 5 = 4 (2.50 m ) / 5
λ 5 = 2.00 m
__             __
8. f1 L1 / √ F1 = f2 L2 / √F2
__       __
f2 = f1L1√F2 /(L2 √ F1)
_____          _____
f2= ((275 hz)(2.50 m)√15.0 N) /((1.50 m) √25.0 N)
f2 = 355 hz

8. (another method)
f1 L1 = f2 L2
f2 = f1 L1 / L2
f2 = (275 hz) (2.50 m) / (1.50 m)
f2 = 458.33 hz
__ __
f2 = f1 √ F2 / √ F1
______ ______
f2 = 458.33 hz √ 15.0 N / √ 25.0 N
f2 = 355 hz

9. v = (331.0 + 0.60 (T)) m/s
v = (331.0 + 0.60 (23)) m/s
v = (331.0 + 13.8) m/s
v = 344.8m/s
f = fo (v + vo) / (v – vs)
f = 5000.0 hz (344.8 m/s + 40.0 m/s) / (344.8 m/s)
f = 5000.0 hz (384.8 m/s) / (344.8 m/s)
f = 5580 hz

10a. fBEAT = |f1 – f2|
fbeat = |412 hz – 416 hz|
fbeat = 4 hz or 4 beats per second

b. T = 1/f
T = 1/4.0 hz
T = 0.25 s = 0.3 s
Cumulative Review #1

Questions
1. For a standing wave, what is a point of zero amplitude called?
2. Name, define and give an example of 4 the 4 properties of all waves.
3. Why will light travel in a vacuum but sound will not?
4. What type of interference results when waves are added 180o out of phase.
5a. If an intensity level increases by 30. db, how much greater is the perceived loudness?
b. If an intensity level increases by 30. db, by how much will the intensity increase?

Problems
1a. What is the wavelength of a wave that travels 340. m/s and has a frequency of 455 hz.
b. What is the period of the wave?
2. What is the period of a pendulum that has a length of 1.0 m on planet earth?
3. What is the length of a pendulum that has a frequency of 0.48 hz?
4a. One person talks with an intensity level of 65.0 db from 1.00m. What would be the intensity level
from 10.0 m?
b. What would be the intensity level of 25 people talking with an intensity level of 65.0 db from 1.00
m?

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