A `75 cm` string fixed at both ends produces resonant frequencies `384 Hz and 288 Hz` without there being any other resonant frequency between these two . Wave speed for the string is

Options

A. `144 m//s`
B. `216 m//s`
C. `108 m//s`
D. `72 m//s`

Answer

A

Explanation

`Delta v = 384 - 288 = 96`
Thus ` 288 and 384 (96 xx 3 , 96 xx 4)` are third and fourth harmonics .
For fundamental mode :
`(lambda)/(2) = 0.75`
`lambda = 1.5`
`eta = 96`
`v = 96 xx 1.5 = 144 m//s`