# Why is the speed of sound in air constant (relative to temperature) when the wave speed formula is Vwave = fλ? [duplicate]

By the logic of the wave speed equation, shouldn't a 1000 Hz sound travel twice as fast as a 500 Hz sound? I know it doesn't, but why not?

## 2 Answers

as frequency goes up, wavelength goes down. their product is constant.

Think of time scales.
There is the time scale for something to change (eg pressure) in a localised region of a gas which is related to the frequency of the wave, eg frequency of oscillation of a loudspeaker cone.
There is the time scale for the information as to what is happening in one localised region to reach another localised region which has something to do with the speed of molecules as the only way that (ideal) gas molecules can communicate with one another is via collisions.

These two time scales are independent of one another ie frequency of oscillation in one localised region does not affect the speed at which information (wave speed) moves from one localised region to another localised region.

What the frequency does change is where in space the pressure of one localised region is $$2\pi, 4\pi$$ etc out of phase with another localised region and the distance between two such localised regions is an integer times a wavelength.
If the frequency increases the distance between such localize regions (wavelength) changes in inverse proportion.
It can be shown that the product of the frequency and wavelength is constant - the speed of the wave.