Question

The figure shows an instantaneous displacement-position graph of a sound wave travelling along the positive $x$ -axis. Identify the points of

maximum pressure;

Accepted Answer

Now, the pressure change in the medium is given by,

$∆ P = - B (\frac{∆ V}{V_{i}})$

where $∆ P =$ The change in pressure

$B =$ The Bulk modulus

$∆ V =$ The change in volume

$V_{i} =$ The initial pressure

Then, for the given displacement position graph the pressure change can be written as:

$∆ P = B (- \frac{d y}{d x})$

Since the pressure change will be positive where the slope $\frac{d y}{d x}$ is negative and the pressure change will be negative where the slope $\frac{d y}{d x}$ is positive.

So, in the given displacement position graph of a sound wave, the points of the maximum and minimum pressure are as follows:

$(1 .)$ The maximum pressure occurs at the point of maximum negative slope at point $A .$

$(2 .)$ The minimum pressure occurs at the points of maximum positive slope at point $C .$

$(3 .)$ The atmospheric pressure remains at the positions of zero slope at point $B .$

Hence, the maximum pressure occurs at the point $A$ as there is a maximum negative slope.

B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS

Questions from B M Sharma Solutions for Chapter: Sound Waves and Doppler Effect, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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