Question

For a certain transverse wave, the distance between two successive crests is 1.20 m and eight crests pass a given point along the direction of travel every 13.50 s. Calculate the wave speed.

Answer 1

Concepts and reason

The concepts used to solve this problem are relation between the frequency and the time period and the relation between the frequency and wave speed.

Initially, use the relation between the time period and the frequency to calculate the frequency of the transverse wave.

Finally, use the relation between the frequency and the wave speed to calculate the speed of the transverse wave.

Fundamentals

The relation between the time period and the frequency of the transverse wave is given by,

Here, f is the frequency of the wave, n is the number of crests passing through a point, and T is the time period of the wave.

The relation between the frequency and the wave speed is given by,

Here, v is the wave speed and is the wavelength of the wave.

The relation between the time period and the frequency of the transverse wave is given by,

Substitute 8 for n and 13.50 s for T in equation as follows:

The relation between the frequency and the wave speed is given by,

Rearrange the equation as follows:

Substitute for f and 1.20 m for in equation as follows:

Ans:

The speed of the transverse wave is .