n number of waves are produced on a string in 0.5 s. Now, the tention in the string is soubled (Assume length and radius constant), the number of waves produced in 0.5s for the same harmonic will be

Options

A. n
B. `sqrt(2)n`
C. `(n)/(sqrt(2))`
D. `(n)/(sqrt(5))`

Answer

B

Explanation

For a stationary wave,
`n=(1)/(2L)sqrt((T)/(m))` . . .(i)
where, T = tension in string
L = length of string
and m = mass of string.
According to the question,
`n'=(1)/(2L)sqrt((T')/(m))`
Here `T'=2T`
`n'=(1)/(2L)sqrt((2T)/(m))rArrn'sqrt(2)(1)/(2L)sqrt((T)/(m))`
From Eq. (i), we get
`n'sqrt(2)n`