Q15CQ - College Physics (Urone)

Question

What is the difference between propagation speed and the frequency of a wave? Does one or both affect wavelength? If so, how?

Step-by-Step Solution

Answer

Propagation Speed is the speed with which the wave moves through the medium. The frequency of the wave is the number of times the wave makes a complete cycle in unit time. Both of them affect the wavelength.

Step 1: Definition of propagation speed

A wave is a disturbance that propagates from the place it was created. The wave speed or the propagation speed is the speed with which this disturbances move in the medium.

Step 2: Definition of frequency

Frequency is the number of times the wave completes one oscillation (up and down motion) in unit time. It is the reciprocal of the time period of wave motion.

Step 3: Relation between propagation speed, frequency, and wavelength

The propagation speed is equal to wavelength times the frequency of wave

         \({\rm{v = f}} \cdot {\rm{\lambda }}\)    

\( \Rightarrow {\rm{\lambda  = }}\frac{{\rm{v}}}{{\rm{f}}}\)

Where, \({\rm{\lambda }}\) is the wavelength, \({\rm{f}}\) is the frequency and \({\rm{v}}\) is the velocity of the wave propagation.

It is seen that wavelength is directly proportional to the propagation speed and inversely proportional to the frequency of wave. Hence, both of them affect the wavelength.