Chapter 25, Problem 9A

How does the speed of a wave relate to its wavelength and frequency?

To determine

To express: The relation of speed of a wave in terms of itswavelength and frequency.

Answer to Problem 9A

The speed of a wave in terms of frequency and wavelength is $v=\lambda \times f$

Explanation of Solution

Introduction:

The speed of any object is the distance travelled by it in a given time.

In the case of a wave, the distance traveled by it is expressed in terms of the wavelength and time is expressed as the reciprocal of frequency.

  

In the above sine wave, the distance for one full cycle is expressed as the wavelength λ, the

velocity of propagation is denoted as the speed with which the wave progresses in the given medium and the frequency is denoted by f which gives the number of cycles completed in one second.

This can be mathematically expressed as,

  $\begin{array}{c}v=\frac{\text{Distance}}{\text{time}}\\ =\frac{\lambda }{t}\\ =\lambda \times f\end{array}$

This gives the relationship between the speed, wavelength and frequency of a wave.