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

The speed of the wave is 309 m/s.

Step-by-step explanation:

The equation given is y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x], where y represents the displacement of a string particle and x represents the position of the particle on the string. The wave is traveling in the +x direction. To find the speed v of the wave, we need to determine the wave velocity. The wave velocity is given by the formula v = ω/k, where ω is the angular frequency and k is the wave number.

In the equation y = (0.0120 m)sin[(927 rad/s)t - (3.00 rad/m)x], the angular frequency is 927 rad/s and the wave number is 3.00 rad/m. Therefore, the wave velocity is v = 927 rad/s / 3.00 rad/m = 309 m/s.

Answer 2

Speed, v = 312.34 m/s

Step-by-step 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=(2\pi)/(\lambda)`

`\lambda=(2\pi)/(3)` ..............(3)

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

Since,
`\omega=2\pi \\u`

`\\u=(927)/(2\pi)`...............(4)

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

`v=\\u* \lambda`

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

`v=(927)/(2\pi)* (2\pi)/(3)`

v = 312.34 m/s

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