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Question

The equation of a travelling sound wave is y =6.0 sin (600 -1.8 x) where y is measured in 105m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.

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Solution

Here given, ry=6.0×105m

(a)Given 2πλ=1.8K

λ=(2π1.8)

So, ryλ=6.0×(1.8)×105m/s(2π)

(b)Let, Velocity Amplitude =Vy

V=dydt

=3600cos(600t1.8x)×105m/s

Here, Vy=3600×105m/s

Again, λ=2π1.8 and T=2π600

wave speed =v

=λT=6001.8=1003m/s

So, The ratio of (Vyv)

=3600×3×1051000


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