Question

A string with linear mass density m $=5.00\times {10}^{-2}$ kg/m is under a tension of 80.0 N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00 cm?

• A. 512 W
• B. 312 W
  
• C. 614 W
  
• D. 215 W
  

Answer 1

Answer: (A)

512 W

Power supplied to a string to generate a sinusoidal wave is given by

$P=\frac{1}{2}\mu w^2{a}^{2}v$

Where, $\mu -$ Mass/length of the string

$\omega -$ angular velocity of the wave

$a-$ amplitude of the wave

$v-$ velocity of the wave

Now, from question,

$\mu =5\times {10}^{-2}ks/m$

$\omega =2\pi \times frequency=2\pi \times 60rad/sec$

$a=6cm=6\times {10}^{-2}m$

$v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{80}{5\times {10}^{-2}}}=40m/s$

$\Rightarrow P=\frac{1}{2}\times (5\times {10}^{-2})\times (4{\pi }^2\times {60}^2)\times (6^2\times {10}^{-4})\times 40$

$\Rightarrow P=512.05\approx 512w$