Question

in an experiment of sonometer it was found that tuning fork and sonometer give 5 beats per second both has length of the wire was 1 m and 0.5 m find frequency of the fork

Answer 1

Given: n1 be the frequency of wire in first case, n2 be the frequency of the wire when the length is 0.5 m.

The fundamental frequency of a streched string is given by the follwing formula.

n=1/2l√T/m

Where

l→Length of the string

T→Tension of the string

m→Mass per unit length of the string

From the above equation, sinceT and m remains constant, we have,

n∝1/l So, n1:n2 = 0.5:1 i.e. n1 = 1*x and n2 = 0.5*x Now using beats, n1 - n = 5 i.e. 1*x - n = 5 (n = fundamental frequency of vibration) And n - n2 = 5 i.e. n - 0.5*x= 5 Adding 1*x - n = 5 and n - 0.5*x = 5 we get, 0.5*x = 10 i.e. x = 20 Hence, we get, n - 0.5(20) = 5 n = 5 + 10 = 15 Hz So, the required frequency of the tuning fork is 15 Hz (Answer)