Question

A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of 50 Hz. The mass of the wire is 30 g and its linear density is `4 xx 10^(-2)` kg m `s^(-1)`. The speed of the transverse wave at the string is
A. `25ms^(-1)`
B. `50ms^(-1)`
C. `75ms^(-1)`
D. `100ms^(-1)`

Answer 1

Correct Answer - C
Here, Mass of the wire, M= 30 g = `30 xx 10^(-3)` kg
Mass per unit length of the wire, `mu=4 xx 10^(-2) kg m^(-1)`
`therefore` Length of the wire,
`L=M/mu=(30xx10^(-3)kg)/(4xx10^(-2)kgm^(-1))=0.75m`

For the fundamental mode,
`lamda=2L=2xx0.75m=1.5m`
Speed of the transverse wave,
`v=upsilonlamda=(50s^(-1)(1.5m)=75ms^(-1)`