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Standard XII

Physics

Intensity of Sound Waves

A source of s...

Question

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is $336 \frac{m}{s}$ ?

1680 Hz

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420 Hz

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840 Hz

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None of these

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Solution

The correct option is B
420 Hz

Intensity is directly proportional to square of pressure amplitude
$I α P_{0}^{2}$

The detector is getting 2 sound waves. One directly from the source and the other after being reflected from the cardboard, these two are interfering at the detector. Now they say that detector was receiving maximum intensity which changed to minimum when cardboard moved by 20 cm.
we know
for maximum intensity constructive interference
for minimum intensity destructive interference

If the cardboard is moved by 20cm then the reflected wave has to travel 40 cm extra. The reflected wave gets a phase difference of π as you can see in the diagram.

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