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The displacement of a string is given by...

The displacement of a string is given by `y(x,t)=0.06sin(2pix//3)cos(120pit)` where x and y are in m and t in s. The lengthe of the string is 1.5m and its mass is `3.0xx10^(-2)kg.`

A

It represents a progressive wave of frequency 60Hz

B

It represents a stationary wave of frequency 60Hz

C

It is result of superposition of two waves of wavelength 3m, frequency 60Hz each travelling with a speed of `180m//s` in opposite directions.

D

Amplitude of this wave is constant.

Text Solution

Verified by Experts

The correct Answer is:
B, C
(a) The given equation is `y(x,t)=0.06 sin ((2pix)/(3))cos(120pit)`
(b) As terms involving x and t are independent of each other, the given equation represents a stationary wave.
(c) Compare the given equation with the standard form of equation of stationar wave:
`y(x,t)=2rsin kxcosomegat`
`k=(2pi)/(lambda)=(2pi)/(3) :. lambda =3m`
`omega=120pi` `:. v=(omega)/(2pi)=(120pi)/(2pi)=60Hz`
and `upsilon=vlambda=60xx3=180m//s`
Hence the given stationary wave is the result of superposition of two waves of wavelength 3m and frequency 60Hz each travelling with a velocity of `180m//s` in opposite directions.
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