IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Interference of Sound

## Introduction

Sound is described by a pressure wave which can be written as $$\Delta p=\Delta p_0 \cos (kx-\omega t+\phi)$$, where $$\Delta p$$ is the change in pressure at $$x$$ at time $$t$$ from the atmospheric pressure, $$\Delta p_0$$ is the maximum change from the atmospheric pressure as the compression and rare faction take place. If two sound waves reach a common place with same frequency, same intensity and a definite phase difference, interference occurs and the intensity becomes $$I=I_0\cos^2 \frac{\phi}{2}$$. Depending on $$\phi$$ the sound intensity can be high or low. This experiment gives qualitative feel of this intensity variation.

## Apparatus

Two audio speakers, a frequency generator to produce a `monochromatic' sound, a stethoscope, measuring tape.

Frequency Generator: The unit gives an electrical voltage that varies at a chosen fixed frequency. The display shows the frequency. Various knobs control the amplitude and frequency of this signal.

Stethoscope: This is the instrument which is identity of a doctor. We will use it as a sound detector.

## Procedure

1. Put the speakers at a distance of say 50-60 cm apart on a table (2.5ft height).
2. Connect the input jacks of the speakers and connect this to the output signal of the frequency generator. The two speaker diaphragms thus vibrate in the same phase, frequency and amplitude.
3. Set the frequency at about 1 kHz.
4. Mark a line parallel to the line joining the speakers at a distance of about 50 cm from it.
5. Put the stethoscope in your ears and let stethoscope disk hang and face towards the speakers. Make sure it is in right orientation so that any small hit on the disk is loudly audible.
6. Stand on the marked line on one side of the speakers at a distance say 1 m from the closer speaker. Make sure you are listening the sound from the speakers.
7. Very slowly shift towards the speakers on the marked line. Watch for the intensity of sound. When you get a minimum intensity, ask your partner to mark the place where you are standing.
8. Keep shifting. The sound intensity will increase and again decrease. Again locate for the place where you get minimum intensity. Mark the place. Mark several such minima to feel interference.

## Discussion

Use the minima positions just on the two sides of the central point. The path difference in the situation shown in figure is

For a minimum this should be $$\lambda/2$$. The value of $$y$$ can be obtained by measuring the distance between two minima on the two sides of the mid points and dividing by two. Calculate the wavelength $$\lambda$$ from this. Calculate the speed of sound in air from $$v=n\lambda$$.

## Note

equations to be verified, figures to be made