A string of length 100 cm has three resonant frequencies, 120 Hz, 200 Hz and 280 Hz. If a node is formed at the end of the string, the speed of the transverse wave on this string is:

Options

A. 60 m/s
B. 80 m/s
C. 100 m/s
D. 120 m/s

Answer

B

Explanation

Given,
Length of string, `L = 100 cm = 1m`
Resonant frequencies of string,
`f _(1) = 120 Hg`
`f _(2) = 200 Hz`
`f _(3) = 280 Hz`
Speed of the transverse wave on string, `V = 2lf_(0)`
` implies V= 2xx 1 xx f_(0)`
`implies V = 2 f _(0)`
`f _(0)-` Fundamental frequency
` = GCD(f_(1) , f_(2), f_(3))`
`= GCD (120, 200, 280)`
`= 40 Hz`
`implies V=2xx 40`
`therefore V = 80 m//s `