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Q.

A sound wave is propagating in air. The wave is represented by $y = 0.01 \sin (150 πt - \frac{π}{2} x)$ where y is in m, x in meter and t is in second. Then ratio of maximum particle velocity to velocity of propagation is

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a

$\frac{π}{200}$

b

$\frac{π}{150}$

c

$\frac{π}{300}$

d

$\frac{π}{75}$

answer is A.

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Detailed Solution

V = Velocity of propagation $= \frac{ω}{k} = \frac{150 π}{π / 2} m / s = 300 m / s$

$u_{\max}$ = Maximum particle velocity = $ω A = 150 π x 0.01 m / s$

$∴ \frac{u_{\max}}{v} = \frac{150 π x 0.01}{300} = \frac{π}{200}$

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A sound wave is propagating in air. The wave is represented by y=0.01 sin 150πt-π2x where y is in m, x in meter and t is in second. Then ratio of maximum particle velocity to velocity of propagation is