Question

A tuning fork vibrating with a sonometer having a wire of length 20 cm produces 5 beats per second.The beats frequency does not change if the length of the wire is change to 21 cm. The frequency the tuning fork must be

Answer 1

Fundamental frequency is:

n = 1/2l √T/m

n 1/l

assume for 20cm frequency is n1

and for 21 cm frequency is n2

So

n1/n2 = 21/20

then n1 = 21x and n2 = 20x

Let frequency nf for producing 5 beats so n1 > nf > n2

So n1 - nf = 5

21x - nf = 5 ....(i)

And nf - n2 = 5

nf - 20x = 5 .....(ii)

from (1) ans (2) we get x = 205 hz