Two sitar strings A and B playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The tension of string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B, if the frequency of A is 427 Hz?

Options

A. 428 Hz
B. 430 Hz
C. 422 Hz
D. 420 Hz

Answer

D

Explanation

Frequency of A is 425 Hz and there are 5 beats with B, hence frequency of B is either 420 Hz or 430 Hz.
When tension (T) is B is increased slightly then its frequency increases according to the following relation :
`f = (1)/(2l) sqrt((T)/(m))`.
Beat frequency is found to be decreased after increasing tension in B, hence original frequency of B must be 420 Hz. Hence option (d) is correct.