Question

The equation that describes a transverse wave on a string is y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x] where y is the displacement of a string particle and x is the position of the particle on the string. The wave is traveling in the +x direction. What is the speed v of the wave?

Answer 1

Answer:

Speed, v = 312.34 m/s

Explanation:

The equation that describes a transverse wave on the string is given by :

$y=0.0120\ msin[(927\ rad/s)t-(3\ rad/m)x]$..............(1)

Where

y = displacement of a string particle

x = position of the particle on the string

The wave is travelling in the +x direction. We have to find the speed of the wave.

The general equation of traverse wave is given by :

$y=A\ sin(kx-\omega t)$................(2)

On comparing equation (1) and (2) we get,

k = 3 rad/m

Since, $k=\dfrac{2\pi}{\lambda}$

$\lambda=\dfrac{2\pi}{3}$ ..............(3)

Also, $\omega=927\ rad/s$

Since, $\omega=2\pi \nu$

$\nu=\dfrac{927}{2\pi}$...............(4)

Speed of the wave is the product of frequency and wavelength i.e.

$v=\nu\times \lambda$

Using equation (3) and (4), the speed of the wave can be calculated as :

$v=\dfrac{927}{2\pi}\times \dfrac{2\pi}{3}$

v = 312.34 m/s

Hence, the speed of the transverse wave is 312.34 m/s