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A sinusoidal wave travels along a taut s...

A sinusoidal wave travels along a taut string of linear mass density `0.1g//cm`. The particles oscillate along `y-` direction and wave moves in the positive `x-` direction . The amplitude and frequency of oscillation are `2mm` and `50Hz` respectively. The minimum distance between two particles oscillating in the same phase is` 4m`.
The amount of energy transferred `(` in Joules `)` through any point of the string in 5 seconds is

A

`(pi^(2))/(10)`

B

`(pi^(2))/(50)`

C

`(pi^(2))/(5)`

D

Cannot be calculated because area of cross`-` section of string is not give.

Text Solution

Verified by Experts

The correct Answer is:
C
`lambda =4m` and `f=500 Hz.`
`:. V=f lambda=200m//s`
`:' V=sqrt((T)/(mu)):. T=mu v^(2)=(0.1)xx(200)^(2)=400N`
Since integral number of waves shall cross a point in 5 seconds, therefore power transmitted in 5 seconds is `= lt P gt xx5=2pi^(2)f^(2)A^(2)mu v xx 5`
`=2xxpi^(2)xx(50)^(2)xx(2xx10^(-3))^(2)xx(0.01)xx200xx5=(pi^(2))/(5)`
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