Question

5 beats/second are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be

Answer 1

The frequency of the fork will be 195 hz

Explanation:

Let the frequency of the sonometer be n

Hence possible frequency = n + 5 or n - 5

=> n + 5 = (1/2*0.95)* √(T/m)

=> n + 5 = (1/1.9)* √(T/m)...............eq1

also

n - 5 = (1/2*1)* √(T/m)

=> n - 5 = (1/2)* √(T/m)

Dividing both the equation we get,

(n+5)/(n-5) = 2/1.9 = 20/19

cross-multiplying both the sides we get

=> 19n + 95 = 20n - 100

=> n = 195

Hence the frequency of the fork will be 195 hz