Traveling waves
21 Wavelength, speed and frequency
Why is wavelength important?
When you make pulses in a medium, every pulse moves away from the source at the same constant speed. If you make pulses at regular time intervals, the result is a “train” of evenly spaced pulses. In technical terms, a periodic vibration creates a wave. The distance between one pulse and the next is the wavelength.
Wavelength explains a lot about how sound works- why tubas must be big, why low frequency sounds are hard to contain, why sonar can locate certain objects (and not others), how dead spots in auditoriums are formed, why instruments produce overtones- the list goes on. This section explains how wavelength is related to the frequency of the wave source and the properties of the medium that the wave travels in.
Wavelength, speed and frequency
When a source with a certain frequency makes waves, each crest travels a certain distance before the next crest is formed. That distance is the wavelength. As a result, wavelength is controlled by just two factors: the frequency of the source and speed of waves.
If sound frequency is low, there’s a a long time between pulses and each pulse travels a long distance before the next one is made. The result is pulses that are spaced far apart- a long wavelength. Shorten the time delay between pulses, and the wavelength gets shorter. (Remember that all waves in the same medium travel at the same speed). The take-away point is that low frequency sources create long wavelength waves and high frequency sources create short wavelengths.
Wavelength is also affected by the medium, because waves travel at different speeds in different media. If the sound travels slow in a particular material, each crest travels only a short distance before the next crest is formed. If the same frequency source makes waves in a medium where sounds travel faster, each crest travels further (in the same amount of time), creating crests that are farther apart (a longer wavelength).
Animations are especially helpful for understanding the concepts in the last two paragraphs. Abbott’s Desmos simulation Pulse Train [1] shows two sources making waves in the same medium. Even though the sources have different frequencies, you can clearly see that both sets of waves travel at the same speed across the screen. You can also see that the high frequency source makes short wavelength waves. Mike Richardson’s youTube video [2] (4:49) uses the PhET simulation “Wave on a string” to show what happens when you change the frequency of a wave source on a string, If you want to try some of the things Richardson shows in the video, you can play with PhET simulation [3] yourself. You will need to check the box at the upper left of the simulation to get rid of the clamp and replace it with the open window- otherwise, you will be exploring standing waves rather than traveling waves.
Here’s the mathematical equation that relates wavelength to wave speed and source frequency:
[latex