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A wave pulse is travelling on a string w...

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by `g(x) = A sin(x /a)`, where A and a are constants. (a) What are the dimensions of A and a ? (b) Write the equation of the wave for a general time 1, if the wave speed is v.

Text Solution

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The correct Answer is:
A, B
At `t=0, g(x)=Asin(x/a)`
a. [M^0L^1T^0]=[L]`
`a=[M^0L^1T^0]=[L]`
b. wave speed =v
`:. Time period T=a/v`
`(a=wave length =lamda)`
`:.` General of wave
`y=Asin{(x/a-t/((a/v))}`
`=AsinP((x-vt))/a}`
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Knowledge Check

  • A wave propagates in a string in the positive x-direction with velocity v. The shape of the string at t=t_0 is given by f(x,t_0)=A sin ((x^2)/(a^2)) . Then the wave equation at any instant t is given by

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    B
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    C
    `g(x,t)=A sin""[x-v(t+t_0)]^2/(a^2)`
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  • The position x of a particle at time t is given by x= (V_(0))/(a)(1-e^(-at)) where V, is a constant and a gt 0 . The dimensions of V_(0) and a are

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