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To determine the speed of sound by using acoustic transducer

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To determine the speed of sound by using acoustic transducer, signal
generator and oscilloscope.
Theory:
In the experiment two transducers T1 and T2 are used (shown in the figure-1).T1 is driven directly by a sine
wave generator and acts as the transmitter (generator of ultrasonic waves) and T2 acts as the receiver.

                                                 T1              T2




                                                                                                   Oscilloscope
  Sine wave generator




                                                          L




                                            Figure-1: Speed of sound by acoustic transducer

Ultrasonic waves are transmitted by the transmitter (T1) and are reflected by the receiver (T2). The two waves
of the same frequency but traveling in opposite direction interfere with each other. The result is the formation
of stationary waves producing alternate points of maximum vibration (antinodes) and minimum vibration
(nodes).

If the receiver is slowly moved away from the transmitter, nodes and antinodes can be seen on the
                                                                       
oscilloscope. Distance between two successive antinodes (or nodes) is     wherefrom λ can be determined.
                                                                       2

The frequency f can be directly read off from the signal generator. The velocity of sound is then given by

v  f                  ..............:....(1)
                                                                                              P
Theoretically we can calculate the velocity of sound in a gas from the relation v 
                                                                                               
 Where P = pressure of the gas
        ρ = density of the gas
             C
        γ = P = ratio of the specific heat at constant pressure to the specific heat at constant volume of
             CV
the gas.
                            5     P RT
For air (diatomic gas)   and 
                            3      M

Where R = molar gas constant
                                                                                                                    2

        T = temperature of the gas in absolute temperature
        M = molar mass of the gas

               5R T
Hence   v          …………………………………………(2)
               3M

Apparatus:

Oscilloscope, sine-wave generator, transducers, slide caliper, connecting wires, etc.

Description of the apparatus:

Acoustic transducer:

Certain crystals (with a permanent electric dipole moment) in response to an applied pressure, develop a
voltage across its opposite surfaces. A longitudinal compression produces a potential difference between the
two surfaces of the crystal in the same direction as the polarizing potential while a longitudinal dilation
produces a reverse voltage.

This effect is utilized in the production of an electrical signal in response to incident ultrasound waves, where
the magnitude of the electric signal varies with the wave pressure of the incident waves. This effect is called
piezoelectric effect.

 Conversely, application of a voltage across the crystal causes deformation of the crystal - either compression
or extension depending upon the polarity of the applied voltage. Potential applied in the same direction as the
polarizing potential shortens the crystal while that applied in the reverse direction lengthens the crystal.

This deforming effect, termed the converse piezoelectric effect, is used to produce an ultrasound beam from a
piezoelectric crystal. A device which converts electrical energy into ultrasound energy and vice versa is
termed as an acoustic transducer.

A number of crystals occurring in nature display piezoelectric properties e.g. quartz, Rochelle salts lithium
sulphate, tourmaline .However crystals used as transducers are almost invariably man made. The most
common man made crystals are barium titanate.

The piezoelectric crystal is the functional component of an acoustic transducer. The crystal usually is
designed as a circular disc. To establish electric contact a pair of electrodes, one in the centre and one around
the edge are evaporated into the crystal which is usually a barium titanate crystal.



Procedure:

 1. Make necessary connections as shown in figure-1. Adjust the frequency of the sine waves round about
    40 103 Hz when pulses will be obtained on the oscilloscope.


 2. Slowly and carefully move away the transducer T2 from T1 and measure the height of the pulse on the
                                                                                                            3

     oscilloscope. Note the corresponding distance between the transducers. In this way go on varying the
     distance between the transducers, each time noting the distance between them and the corresponding
     pulse height.


 3. Plot a graph with the distance L (between the transducers) as the abscissa (X-axis) and pulse height
    as the ordinate (Y-axis). A graph similar to one shown in the figure-2 will be obtained.




                          Figure-2: Pulse height vs. distance between transducers

 4. Measure λ from the graph. Hence calculate  .

 5. Note the room temperature both before and after the experimen. Calculate  theoretically with the
    help of equation (2) and compare the two values of speed of sound.

Discussions:

The experimental value of the velocity of sound as determined from this experiment is………………m/sec.
The theoretical value as calculated is…………………….. m/sec. The two values should be in good
agreement.


Data Sheet:

Table for pulse height at different distances between the two transducers:

Distance between the           Pulse height               Distance between the       Pulse height
  two transducers                                           two transducers

        (mm)                 (arbitrary unit)                     (mm)              (arbitrary unit)
                                                                                 4




Calculation:


                                                                       
      Number Distance   Wave     Frequency    Speed   Mean                   2

        of   between    length                  of            
       peaks   the                   f        Sound                  n 1
              peaks                            f
                                                                                                       5

               n     L            2L                   (m/s)
                                                                    (m/s)             (m/s)
                   (mm)            n       (Hz)
                              (mm)

1.


2.         3                             40 103

3.



Theoretical Calculation:

We consider air as a mixture of two diatomic gases- 80% of nitrogen (N2) and 20% of oxygen (O2) . Now the
molar mass of N2 and O2 are 28 gm/mol and 32 gm/mol.

      28  80  32  20
M                      gm / mol  28.8 gm / mol  28.8  10 3 kg / mol .
            100
Gas constant, R = 8.31 J/K

Room temperature before experiment in absolute temperature = ……………….

Room temperature after experiment in absolute temperature = ……………….

Mean room temperature, T =…………………….
                             5R T
Hence speed of sound   v            = …………………….
                             3M

Results:

Experimental value of speed of sound,      ………………           ……………….


Theoretical value of speed of sound,     ………………………

Pre-Lab Exercise:

1. What is acoustic transducer?
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2. What is stationary wave?

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3. In a stationary ultrasound wave in air, the distance between two consecutive antinodes is 4.5 mm and the
   frequency of the ultrasound wave is 40KHz. What is the speed of sound wave in air?

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4. How does the speed of sound in air depend on temperature?

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5. Does the speed of sound in air depend on pressure and density of air?

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posted:3/3/2013
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