A tuning fork of frequency 480 Hz produces 10 beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before

Options

A. 480 Hz
B. 490 Hz
C. 470 Hz
D. 460 Hz

Answer

C

Explanation

Since there are 10 beats/s, the frequency of the string `(n_(s))` may be `(480 -+ 10)`i.e, 490 Hz or 470 Hz.
If the tension is increased, `n_(s)` is increased
If `n_(s) = 490 Hz, n_(s) " will be " gt 490` Hz and no. of beat/s will increase. But it is given that the no. of beats/s is decreased. Hence it should be 470 Hz.
[If it becomes 475 Hz, then `480 - 475 = 5`, i.e. no. of beats/s is decreased from 10 to 5]