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Question

For the wave shown in the figure, write the equation of the wave if its position is shown at t=0 speed of wave is 200 m/s.

A
y(x,t)=0.12sinπ[x2000 t] m
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B
y(x,t)=0.12sin[31.4 x6200 t] m
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C
y(x,t)=0.12sin[3.14 x6283 t] m
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D
y(x,t)=0.12sin[31.4 x6283 t] m
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Solution

The correct option is D y(x,t)=0.12sin[31.4 x6283 t] m
From the figure, we can deduce that,
Amplitude (A)=0.12m
32λ=0.3
λ=2×0.33=0.2 m
frequency (f)=vλ=2000.2=1000 Hz
Angular wavenumber (k)=2πλ=2π0.2=31.4 m1
and ω=2πf=2π×10006283 rad/s

At t=0,x=0,dydx=+ve
Therefore given curve is a sine curve
Hence, equation of wave travelling in positive x-direction should have the form

y(x,t)=Asin(kxωt)
Substituting the obtained values, we get
y(x,t)=0.12sin[(31.4 x6283 t] m
Thus, option (d) is the correct answer.

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