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Question

A longitudinal wave propagating in a water-filled pipe has intensity 3.00 × 106 wm2 and frequency 3400 Hz. Water has density 1000 kgm3 and bulk modulus 2.18 × 109 Pa. If the pipe is then filled with air at pressure 1.00 × 105 Pa and density 1.20 kgm3, and the a wave with the same intensity and frequency is propagated, What is the ratio of the two amplitudes in both media?


A

4

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B

2.25

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C

1.75

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D

None of these

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Solution

The correct option is B

2.25


I = 2π2 A2 f2 pV

Forwater3.00 × 106 = 2π2 × A2 × (3400)2 × v

v = Bp = 2.18 × 1091000

A2 = 3.00 × 106 × 10002π2 × (3400)2 × 2.18 × 109

Aω = 2.99 × 109m

3 nm

For air

3.00 × 106 = 2π2 × A2 × (3400)2 × 1051.2

Aω = 6.75 × 109m

Now AaAω = 6.753 = 2.25


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