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Chapter 2: Q15DQ (page 497)

Can a standing wave be produced on a string by superposing two waves traveling in opposite directions with the same frequency but different amplitudes? Why or why not? Can a standing wave be produced by superposing two waves traveling in opposite directions with different frequencies but the same amplitude? Why or why not?

Short Answer

Expert verified

A standing wave is not produced by the superposition of two waves of different amplitudes or with different frequencies.

Step by step solution

01

Concept of Nodes and antinode

A standing wave is an interference phenomenon in which some points called nodes never moved at all while some points midway between the nodes called anti-nodes vibrate with the maximum amplitude.

A standing wave is formed when two identical waves traveling in the opposite direction superimpose. A wave traveling in a string gets reflected back from the fixed end of the string and superimpose with the incident wave to form a standing wave.

02

The conditions for the standing wave to form are:

The frequency of both the waves should be the same and the wavelength of the two waves should be the same. The amplitude of both the waves should also be equal, and waves should travel in the opposite direction.

Therefore, a standing wave is not produced by superposition of two waves of different amplitudes or with different frequencies.

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