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The vibrations of string of length 60 cm...

The vibrations of string of length `60 cm` fixed at both ends are presented by the equations
` y = 4 sin ( pi x//15) cos ( 96 pi t)`
where `x and y` are in cm and t in `s`. The maximum displacement at `x = 5 cm` is

A

`2 sqrt(3) cm`

B

`4 cm`

C

zero

D

`4 sqrt(2) cm`

Text Solution

Verified by Experts

The correct Answer is:
A
For ` x = 5 , y = 4 sin ((5 pi)/( 15)) cos (96 pi t)`
` = 2 sqrt(3) cos (96 pi t)`
So , `y` will be minimum when `cos (96 pi t ) = max = 1`
`y_(max) = 2 sqrt(3) "cm at" x = 5`
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