Intensity of Sound
Commonly measured in Decibels (dB), the relative intensity of sound is based on a logarithmic scale, much
like the Richter scale for measuring earthquakes and the pH scale for measuring acidity.
The equation for measuring the relative intensity of sound is:
dB = 10 Log
where I0 = 10 W/cm which is known as the threshold of hearing, or the lowest level of sound the
“average” person can hear.
1. What is the relative intensity of a sound which has an intensity of 10-9 W/cm2?
2. What is the intensity of a sound which has a relative intensity 110 dB?
3. A pneumatic drill has the same intensity at 2 feet away as a jet plane’s engine has a 1000 ft away, 200
dB. What is the intensity of this sound in W/cm2?
Moving Source, Stationary Observer:
Source approaching the listener; Source moving away from the listener;
[aka listener in front (Lf)] [aka listener behind (Lb)]
fLf = fs V fLb = fs V
V V V V
Stationary Source, Moving Observer:
Listener approaching the source; Listener moving away from the source;
[aka listener closing (Lc)] [aka listener opening (Lo)]
V Vs V Vs
fLc = fs
fLo = fs
1. While you are sitting at a railroad crossing waiting for an approaching train, the engineer sounds the
whistle (f = 500 Hz).
a. If the train is approaching at 20 m/s and the air temperature is 20 C, what frequency will you
b. After the train passes you the whistle sounds again, now what frequency will you hear?
2. You are driving through the neighborhood and pass a car whose alarm is going off (f = 700 Hz).
a. If you are obeying the speed limit of 25 mph (11.3 m/s), what frequency will you hear as you
approach the car?
b. What frequency will you hear after you pass the car?
3. On the freeway, you are driving at a law abiding 60 mph (100 km/h) when an obnoxious driver passes
you at 80 mph (133 km/h) blowing his horn (f = 100 Hz), what frequency will you hear as he passes
you? (hint: with what relative velocity does he pass you, naturally if he is obnoxious the driver is male)