Question

Of the following properties of a wave, the one independent of the others is:

• A. Amplitude
• B. Velocity
• C. Wavelength
• D. Frequency

Hint:

Recall v equals f times wavelength, then check which listed quantity is missing from that equation.

Answer 1

The Correct Option is A

Imagine shaking one end of a long stretched string to send a wave along it.

• If the tension and mass per unit length of the string stay fixed, the wave speed on the string is fixed by the string itself, not by how you shake it.
• Shake the string faster, meaning a higher frequency, and since $v = f\lambda$ must still hold with $v$ fixed, the wavelength $\lambda$ has to shrink to compensate. So frequency and wavelength are locked together once speed is fixed.
• Now shake the same string with the same frequency but harder, giving it a bigger swing. The wave still travels at the same speed with the same frequency and wavelength, only the size of the swing, the amplitude, changes.

This shows amplitude can be changed freely without disturbing the fixed relationship between velocity, frequency and wavelength, so amplitude is the property independent of the rest, option A.