Question Video: Relating the Frequency of a Sound Wave to Its Wavelength

What frequency sound has a 0.10-m wavelength when the speed of sound is 340 m/s?


Video Transcript

What frequency sound has a 0.10-meter wavelength when the speed of sound is 340 meters per second?

Let’s call the value of 0.10 meters, the wavelength, πœ†. And we’ll call the speed of sound, 340 meters per second, 𝑣 sub 𝑠. We want to solve for the frequency associated with these two values; we’ll call that frequency 𝑓.

In this example, the relationship that helps us connect these three terms has to do with wave speed. And since sound is a wave, it obeys this equation which says that wave speed 𝑣 is equal to wave frequency 𝑓 times wavelength πœ†. When we apply this relationship to our scenario, it’s the speed of sound, 𝑣 sub 𝑠, that is equal to wave frequency, 𝑓, we want to solve for times wavelength, πœ†.

If we rearrange this equation to solve for 𝑓, we see that it equals the speed of sound 𝑣 sub 𝑠 divided by πœ†. Plugging in for those two values, when we calculate this fraction, we find that the frequency 𝑓 is equal to 3.40 thousand hertz or kilohertz. That’s the frequency associated with this wavelength and wave speed.

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