A wire tension 225 N produces 6 beats per second when it tuked with a fork, when the tension changed to 256 N, it again tuned with the same tuning fork to no. of beats remained unchanged, the frequency of tuning fork will be :

A wire tension 225 N produces 6 beats per second when it tuked with a fork, when the tension changed to 256 N, it again tuned with the same tuning fork to no. of beats remained unchanged, the frequency of tuning fork will be : Correct Answer 186

Concept:

The frequency of a tuning fork is directly proportional to the square root of tension applied to it.

f ∝ √T;

or f = K √T;

The number of beats = difference between frequencies of two superimposed waves.

Calculation:

Let the frequency of tuning fork = f_T;

When wire tension = 225 N ⇒ f_w = K√225 = 15K; 

no. of beats = 6 ⇒ f_T - f_w = 6 

⇒ fT = 6 + 15K;   - (1)

When wire tension = 256 N ⇒ fw = K√256 = 16K; 

no. of beats = 6 ⇒ fw - fT = 6 

⇒ fT = 16K - 6;   - (2)

From the equations 1 and 2,

K = 12 ⇒ f_T = 186;