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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 progresssive wave of frquency 60Hz

B

It represens a stationary wave of frequency 60Hz

C

It is the result superpositon of two waves of wavelength 3m , frequency 60 Hz each travelling with a speed of 180 m/s in ipposite direction

D

Amplitude of this wave is constant

Text Solution

Verified by Experts

The correct Answer is:
B, C
Given equation is `" " y(x,t)=0.06 sin ((2pix)/(3)) cos (120pit)`
(a) Comparing with a standard equation of staionary wave
`" " x(x,t)=a sin (kx) cos (omegat)`
Clearly, the given equation belongs to stationary wave. Hence , options (a) is not correct.
(b) By comparing.
`rArr" " omega=120pi`
`" " 2pif==120pirArrf=60Hz`
(c) `k=(2pi)/(3)=(2pi)/(lambda)`
`rArr" " lambda` = wavelength =3m
`" "` Frequency =f=60Hz
`" "` speed = `flambda` =(60Hz)(3m)=180m/s
(d) Since in stationary wave, all particless of the medium execute SHM with varying amplitude nodes.
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