Question

How are the wavelength and the frequency of a sound wave related to its speed?

Answer 1

Answer:

20 Hz

For sound waves in air, the speed of sound is 343 m/s (at room temperature and atmospheric pressure). The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are thus between approximately 17 m and 17 mm, respectively.

Explanation:

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Answer 2

The formula goes:

λ=vf

Where λ is the wavelength, v the speed of sound in the medium, f the frequency of the source generating the waves.

So on one end you have a source of disturbance. This source is perturbing some quantities (in the cause of sound, the local air pressure) in its close neighbourhood. The nature of the perturbation is rhythmic, or cyclic, or periodic: it repeats itself for f times in a second.

Now, the perturbation is such that it has the ability to spread across space, and it does it with a certain speed, v.

Now, we said that the source repeats f times in a second. That’s equivalent to say that one repetition lasts T=1f seconds.

During that time, T, the perturbation will have travelled a certain space, which is given by velocity multiplied by time, right? So we have:

λ=T⋅v=vf

After that length of space, given that the velocity is constant, and the frequency as well, everything will have to repeat with the same pattern. Indeed, λ is the wave periodicity in space.

Hope it makes sense.