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 $100m{s}^{-1}$, what average power is the source transmitting to the wire ?

Answer 1

$r=0.5mm$

$=0.5\times {10}^{-3}m,$

$f=100Hz$

$T=100n,V=100m/s$

$v=\sqrt{\left(\frac{T}{m}\right)}$

$\Rightarrow v^2=\left(\frac{T}{m}\right)$

$\Rightarrow m=\frac{T}{v^2}=\frac{100}{(100{)}^2}$

$=0.01=0.01kg/m$

$P_{ave}=2{\pi }^{2}mv{r}^2{f}^2$

$=2\left(3.14{)}^2\right(0.01)\times 100\times (0.5\times {10}^{-3}{)}^2\times \left(100\right)$

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

$=19.7\times 0.0025=0.049watt$

$=49\times {10}^{-3}watt=49mW$