Question

A string along which waves can travel is 4.29 m long and has a mass of 228 g. The tension in the string is 31.1 N. What must be the frequency of traveling waves of amplitude 6.83 mm for the average power to be 47.1 W

Answer 1

Answer:

200 Hz.

Explanation:

given,

Length of the string,L = 4.29 m

Mass of the string,m = 228 g

Tension of the string,T = 31.1 N

frequency of travelling, f = ?

Amplitude of the wave,A = 6.83 mm

Average Power,P = 47.1 W.

we know,

$P_{avg}=\dfrac{1}{2}\mu v\omega^2 A^2$

we know,

     $v=\sqrt{\dfrac{T}{\mu}}$

       $\omega = 2\pi f$

        $\mu = \dfrac{M}{l}=\dfrac{0.228}{4.29}= 0.05315\ kg/m$

inserting all the values

$P_{avg}=\dfrac{1}{2}\times\sqrt{\mu T}\times (2\pi f)^2 A^2$

$47.1=\dfrac{1}{2}\times\sqrt{31.1\times 0.05315}\times (2\pi f)^2\times A^2$

$f=\sqrt{\dfrac{47.1\times 2}{\sqrt{31.1\times 0.05315}\times 0.00683^2\times4\times \pi^2}}$

f = 199.46 Hz

Hence, the frequency of wave is equal to 200 Hz.