What is the speed of sound in a medium where a 100-kilohertz frequency produces a 5.96-centimeter wavelength?
For the frequency of 100 kilohertz, we’ll give that the name 𝑓. And for the wavelength of 5.96 centimeters, we’ll call that 𝜆. We want to know the speed of sound given this information; we’ll call that 𝑣.
Let’s start our solution by recalling that sound is a wave, and therefore the speed of sound follows the equation for the speed of a wave. This equation tells us that the wave speed 𝑣 is equal to the wave frequency multiplied by its wavelength. When we apply this relationship to our scenario, since we’ve been given both 𝑓 and 𝜆, we can plug those values into this equation.
As we do, the important point to remember is to convert the units of frequency into hertz and the units of wavelength into meters. When we do that we have 1.0 times 10 to the fifth hertz as our frequency and, for our wavelength, 5.96 times 10 to the negative two meters.
Multiplying these values together gives us a speed of sound of 5.96 times 10 to the third. That’s the speed of sound in a medium with these properties.