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

Answer

D

Explanation

frequency `(f)=(1)/(2l)sqrt((T)/(mu))`
`implies 416=(1)/(2l)sqrt((4g)/(mu))...(i)`
`l.=2l, M.rarr` new load
Fundamental mode is same
`f.=f=416=(1)/(2l.)sqrt((gM.)/(mu))`
`implies416=(1)/(4l)sqrt((M.g)/(mu))...(ii)`
From eq. (i) & (ii) M. = 16 kg.