Question

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

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

Step-by-step solution

Given Data

Two waves travel on the same string

Concept

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

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.