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

We use power transmitted is given as
`P = (1)/(2)muomega^(2)A^(2) v` Using `V = sqrt((T)/(mu))`
`P = (1)/(2)omega^(2)A^(2)sqrt(T mu)`
`omega = sqrt((2p)/(A^(2)sqrt(Tmu)))`
`f = (omega)/(2pi) = (1)/(2pi) sqrt((2p)/(A^(2)sqrt((Tmu)))`