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Chapter 2: Q1DQ (page 496)

Two waves travel on the same string. Is it possible for them to have (a) different frequencies; (b) different wavelengths; (c) different speeds; (d) different amplitudes; (e) the same frequency but different wavelengths? Explain your reasoning.

Short Answer

Expert verified

Options (a), (b) and (d) are correct.

Step by step solution

01

Given Data

Two waves travel on the same string

02

Concept

If the two waves travel on same string, they will have different frequencies.

03

Explain the reasoning

  • Yes, it is possible to have two different waves of different frequencies on a string (Imagine driving the string with a square wave; it consists of multiple frequencies with multiple amplitudes; See Fourier transform).
  • However, the velocity of waves on a thin string is constant and depends only on the tension of the string and the density. Thus, you cannot have waves of different speeds.
  • Thus, you can have waves of different frequencies, amplitudes and wavelengths, but you cannot have waves of different speeds.

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