Question

If you increase the frequency of a sound wave four times, what will happen to its speed?
The speed will increase four times.

The speed will decrease four times.

The speed will remain the same.

The speed will increase twice.

The speed will decrease twice.

Answer 1

`Wave Equation:`
\[\huge v=f \lambda\]
v=velocity
f=frequency
\(\lambda\)=wavelength

Answer 2

Careful. That equation can lead you to the wrong answer, if you don't know a few things.

It's true that the speed of a wave is equal to it's wavelength times it's frequency, but this isn't necessarily useful when answering this question.

In the real world, the speed of sound in a material may have some frequency dependence. This effect tends to be small, however, and is generally ignored. That is, the speed of sound in a uniform medium is constant.

It is, however, a function of the density of the material. v = sqrt(K/rho), where K is called the "bulk modulus" of the material, and rho is the density. Notice that neither of those things depends on the frequency of the incoming sound. Density is effected by temperature, though (K can be, as well, so it can get a bit complicated).

The take away is that, unless you are talking about very small changes in the speed of sound of a system that has frequency dependence, the speed of sound is independent of the frequency of the wave. That is, changing the frequency of the sound wave will not result in a different speed of sound. It will, however, result in a different wavelength, as governed by the equation: speed = wavelength * frequency