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Question

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given by f(t) = A sin(tT) The wave speed is v. Write the wave equation.


A

y=A sin(tTxvT)

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B

y=A sin(2πtT2πxvT)

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C

y=A sin(xvT)

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D

None of these

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Solution

The correct option is A

y=A sin(tTxvT)


We are given f(t) = A sin (tT)

Which implies the amplitude is A and comparing it with standard

SHM equation (y = A sin ωt)

We get ω= 1T

Now we know a sinusoidal wave moving in +ve x direction looks like y = A sin (kx - ωt) or y = A sin (ωt - kx) [Basically the signs of the two terms containing x and t respectively must be opposite]

Alsok=ωv=1vT

for given wave equation is y=A sin(tTxvT)


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