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, 𝜆. 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 𝜆. 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, 𝜆.
If we rearrange this equation to solve for 𝑓, we see that it equals the speed of sound 𝑣 sub 𝑠 divided by 𝜆. 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.