The range of human hearing extends from approximately 20 Hz to 20000 Hz. Find the wavelengths of these extremes when the speed of sound in air is equal to 330 m/s.

Answer 1

There is an equation to relate wavelength to speed and frequency, λ=v/f (wavelength = velocity / frequency)

But really, you don't need a memorized equation to solve this, I'd just look at the units. Frequency is in Hz, which is the same as 1/s, and the speed we've been given is in m/s. A wavelength is in distance units, so meters in this case.

Now we're using m/s and 1/s to get m, so we can divide m/s (speed) by 1/s (Hz) to get meters, which of course is the same setup as plugging into the equation.

For the low end of the range 20 Hz, we can use (300 m/s) / (20 1/s) to get 15 m.

The 20000 Hz has the same speed, only frequency is different. (300 m/s) / (20000 1/s) = 0.015 m

To check your work, remember that lower frequencies should have a longer wavelength, and higher frequencies have a shorter wavelength. What we found here fits that, so this answer looks reasonable.