Question

In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be:

(1) 537 Hz 

(2) 523 Hz 

(3) 524 Hz 

(4) 536 Hz

Answer 1

Correct answer is (3) 524 Hz

Guitar string i.e. string is fixed from both ends

Frequency ∝ √(Tension) 

If tension in B slightly decrease then frequency of B decrease.

If B is 536 Hz, as the frequency decreases, beats with A also decreases. 

If B is 524 Hz, as the frequency decreases, beats with A increases.

∴ original frequency of B will be 524 HZ.