Two waves `y_(1) = A cos (0.5 pi x - 100 pi t)` and `y_(2) = A cos (0.46 pi x - 92 pi t)` are travelling in a pipe placed along the `x ` - axis.
Find wave velocity of louder sound

Options

A. `100`
B. `46`
C. `192`
D. `96`

Answer

A

Explanation

At `x = 0`
`y = y_(1) + y_(2) = A cos (100 pi t) + A cos ( 92 pi t)`
`rArr y = 2 A cos ( 96 pi t) sin ( 4 pi t)`
for `y = 0` , we have `sin ( 4 pi t) = 0`
`rArr t = (n)/(4)`
`rArr t = 0 , (1)/(4) , (2)/(4) , (3)/(4) ,(4)/(4) "in" 1 s`
This is ` 5` times
also for `y = 0` , we have `cos ( 96 pi t) = 0`
`rArr 96 pi t = (( 2m - 1) pi)/( 2)`
`rArr t = ( 2m - 1)/( 192)`
`rArr t = (1)/(192) , (3)/(192) ,....,(191)/(192)`
This is `95` times.
So the total number of times , the value of `y = zero is 100`.