Question

A transverse wave of amplitude 0⋅50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 m s−1, what average power is the source transmitting to the wire?

Answer 1

Average Power is 49mW  

Explanation:

Given,

Amplitude of the transverse wave, r = 0.5 mm =$0.5 \times10^-^3\ m = 0.5\times10^-^3\ m$

Frequency, f = 100 Hz

Tension, T = 100 N

Wave speed, v = 100 $ms^-1$

Thus, we have:

$\nu = \sqrt (T/m)$

$\nu = \frac {T}{m}$

m = $\frac {T}{\nu^2}$

= $\frac {100}{100^2}$

= $0.01 kgm^-^1$

Average Power of Source:

$P_a_v_g = 2\pi^2m\nur^2f^2$

= $23.14^2(0.01)\times100\times (0.5 \times 10^-^3)^2 \times 100$

= $2 \times 9.86 \times 0.25 \times 10^-^6 \times 10^4$

= $19.7 \times0.0025 = 0.049 W$

= $49 \times 10^-^3 W$ = 49mW