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
Three resonant frequencies are given as
` f_1 = 120 Hz, f_2 = 200 Hz, f_3 = 280 Hz`
` because` Fundamental frequency `(f_0 )` is equal to the greatest common factor of `f_1, f_2 " and " f_3 ` .
` therefore f_0` = greatest common factor of 120 Hz, 200 Hz and 280 Hz i.e., ` f_0 = 40 Hz`
Now, we know that, speed of transverse wave is given by `v = 2l f_0 = 2 xx 1 xx 40 = 80 m//s`