Sinusoidal waves `5.00 cm ` in amplitude are to be transmitted along a string having a linear mass density equal to `4.00xx10^-2kg//m`. If the source can deliver a maximum power of `90W` and the string is under a tension of `100N`, then the highest frequency at which the source can operate is (take `pi^2=10`)

Options

A. 45.3 Hz
B. 50 Hz
C. 30 Hz
D. 62.3 Hz

Answer

C

Explanation

`P=(1)/(2)muomega^(2)A^(2)V` using `V=sqrt((T)/(mu))`
`P=(1)/(2)omega^(2)A^(2)sqrt(Tmu)`
`omega=sqrt((2P)/(A^(2)sqrt(Tmu))),f=(omega)/(2pi)=(1)/(2pi)sqrt((2P)/(A^(2)sqrt(Tmu)`
using the given data, we get f=30 Hz.