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A plane longitudinal wave having angular frequency $ω = 500 rad / sec$ is travelling in positive x-direction in a medium of density $ρ = 1 kg / m 3$ and bulk modulus $4 × 104 N / m 2$ . The loudness at a point in the medium is observed to be 20 dB. Assuming at x = 0 initial phase of the medium particles to be zero, find the equation of the wave.

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y = 2 × 10 − 9 sin 500 t − 5 x 2

$y = 3 \times 10^{- 9} \sin (500 t - \frac{5 x}{2})$

y = 3 × 10 − 9 sin 500 t + 5 x 2

y = 2 × 10 − 9 sin 5000 t − 5 x 2

answer is A.

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Detailed Solution

ϑ = B ρ = 200, K = w ϑ

K = 500200 = 52

20 = 10 log I I 0 ⇒ 10 = 10 log I I 0 1 / 2

I = 100 I 0 = 100 × 10 − 12 w / m 2

I = 12 δ A 2 W 2 → A = 2 × 10 − 9 m ∴ y = 2 × 10 − 9 sin 500 t − 52 x

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