A sonometer wire supports a 4 kg load and vibrates in fundamental mode with a tunig fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to

Options

A. 1kg
B. 2kg
C. 4kg
D. 16kg

Answer

D

Explanation

Load supported by sonometer wire = 4 kg
tension in sonometer wire =4g
IF `mu`= mass per unit length
then frequency `v=1/(2l)sqrt(T/mu) implies 416=1/(2 l) sqrt((4g)/mu)`
when length is doubled, i.e., l.=2l
Let new load =L
As v.=v
`1/(2l).sqrt((Lg)/mu)=1/(2l)sqrt((4g)/mu) implies 1/(4l) sqrt((Lg)/mu)=1/(2l) sqrt((4g)/mu)`
`implies sqrtL=2 times 2 implies L=16 kg`