Question

a sonometer wire support a 4 kg load and vibrate in fundamental mode with A tuning fork of frequency 416 Hz the length of wire between the bridges is now double in the order to maintain our fundamental mode the load should be changed to​

Answer 1

Answer:

16 Kg

Explanation:

For the given problem ,

T−−√l=constant

or T∝l2

If l is to be doubled , T would be quadrupled.

Answer 2

Answer: load should be 16kg

Explanation:

For a sonometer wire,

f=1/2l *√T/u

f - frequency, T- tension, u- mass per unit length , l - length of wire b/w the 2 bridges

Act question

f1 = f2

Therefore

(1/2l)*√T/u = (1/2* 2l) √T'/u

On Cancelling the terms

√T= (1/2 ) √ T'

T=T'/4

T'= 4T

Now T = mg

Therefore

m'g = 4 mg

Hence

m' = 4m

m' = 4*4

m' = 16