A violin string oscillation in its fundamental mode, generates a sound wave with wavelength `lamda`. To generate a sound wave with wavelength `(lamda)/(2)`. By the string still oscillating is its fundamental mode, tension must be changed by the multiple.

Options

A. 2
B. `1//2`
C. 4
D. `1//4`

Answer

C

Explanation

`v alphasqrt(T)` and as there is no change in length
`lambdaalpha (1)/(sqrt(T))`
`(lambda')/(lambda) = sqrt(T)/(sqrt(T'))`
implies `sqrt(T) = (lambda)/(lambda')sqrt(T)`
implies `T' = (2)^(2) T = 4T.