Question

Two sitar strings A and B playing the note ‘Gd’ are slightly out of tune and produce beats of frequency 6 Hz. The tension In the string A Is slightly reduced and the beat frequency Is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what Is the frequency of B?

Answer 1

Let f₁ and f₂ be the frequencies of strings A and B respectively. 

Given:

f₁ = 324 Hz

Beat frequency = f_b = 6 Hz 

∴ f₂= f₁ ± f_b =(324 ±6) Hz 

We know that T ∝ v² and v ∝ f 

(∵ T = μv² and v = fλ.)

Thus f ∝ √T…………(1)

Decreasing the tension in string A will decrease the frequency f₁. Since the beat frequency f_b is reduced to 3 Hz upon decreasing the tension in string A, f₂ = 318 Hz.

Note: 

If f₂ = 330 Hz, then the beat frequency would have increased when the tension in string A was reduced.