A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrtor. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :

Options

A. `320 ms^(-1), 120 Hz`
B. `180 ms^(-1), 80 Hz`
C. `180 ms^(-1), 120 Hz`
D. `32 ms^(-1), 80 Hz`

Answer

D

Explanation

Frequency of third harmonic, `f_(3) = (3v)/(2L) = 240 Hz`
`rArr (3v)/(2 xx 2) = 240 Hz`
`rArr v = 320 ms^(-1)`
Fundamental frequency, `f_(0) = v/(2L) = 320/(2 xx 2) = 80 Hz`