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.`

Options

A. It represents a progressive wave of frequency 60 Hz.
B. It represents a stationary wave of frequency 60 Hz.
C. It is the result of superposition of two waves of wavelength 3m, frequency 60 Hz each travelling with a speed of 180 m/s in opposite direction.
D. Amplitude of this wave is constant.

Answer

B, C

Explanation

The given equation is `y(x, t) = 0.06 sin ((2pi x)/(3)) cos 120 pi t" "…(i)`
The general equation of stationary wave is `y(x, t) = 2r sin kx cos omega t" "…(ii)`
Comparing equation (i) and (ii), we get
`k = (2pi)/(lambda) = (2pi)/(3)"so" lambda = 3` m
`omega = 120 pi`
`v = (omega)/(2pi) = 60` Hz
`upsilon - v lambda = 60 xx 3 = 180 ms^(-1)`
The correct option are (b) and (c).