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A transverse harmonic wave on a string i...

A transverse harmonic wave on a string is descrbed by `y(x, t) = 3.0 sin (36 t + 0.018 x + pi/4)` where x and y are in cm and t is in s. The position direction of x is from left to right.

A

The wave is travelling from right to left.

B

The speed of the wave is `20m//s`

C

Frequency of the wave is 5.7 Hz

D

The least distance betweent two successive crests in the wave is 2.5cm

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
The given equation is `y(x,t)=3.0sin [36t+0.018x+(pi)/(4)]`
(a As positive direction is from left to right and x positive, therefore, wave is travelling from right to left.
(b) Compare the given equation with the standard form
`y=rsin[(2pit)/(T)+(2pix)/(lambda0+phi)]`
`(2pi)/(T)=36, (2pi)/(lambda)=0.018`
speed of wave, `upsilon=(lambda)/(T)=(36)/(0.018)=2000cm//s=20m//s`
(c) Again, `T=(2pi)/(36)=(pi)/(18)`
Frequency, `v=(1)/(V)=(18)/(pi)Hz=5.7Hz`
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