Speed of Sound

- If we let a speaker make one short burst, we'll create a pulse wave. We can find the speed of sound by looking at the speed of this compressed region as it travels through the medium. In non-humid air at 20 degrees Celsius, the speed of sound is about 343 meters per second or 767 miles per hour. We can also watch the speed of sound of a repeating simple harmonic wave. The speed of the wave can again be determined by the speed of the compressed regions as they travel through the medium. Note that the speed of sound does not mean the speed of the air molecules as they move back and forth. The air molecules are moving with the speed, but by the speed of sound, we mean the speed of the disturbance as it moves through the air molecules. We call sound a longitudinal wave because the wave is traveling parallel to the line traced out by the oscillations of the medium. The other type of wave is a transverse wave. Transverse waves happen when the wave velocity points perpendicular to the oscillations of the medium. Waves on a string or waves on the surface of water are examples of transverse waves. If we look at a graph of the air displacement versus position of the air, we can see that as the wave travels the shape of this wave travels to the right. So, the speed of a sound wave can be found by finding the speed of the peaks or the speed of the valleys or the speed of any single point on the wave shape. To figure out a formula for the velocity of a sound wave, let's look closely at what's happening here. Watch one of the air molecules. It takes one period for this molecule to move back and forth through a full cycle. During this time, the wave shape has moved forward one complete wavelength. This is because the wave has to overlap with its initial shape after one period, because the molecule has to be back where it started after one period. Now, since speed is defined to be the distance per time, the speed of a sound wave has to be the wavelength of the wave divided by the period of the wave. Since the wave is traveling forwards one wavelength per period, or since the frequency is defined to be one over the period, we can rewrite this formula as speed equals wavelength times frequency. This formula is accurate for all kinds of waves, not just sound waves, because a wave has to move one wavelength for every period. Be careful. When looking at this equation, you might think that if you adjust the setting on your speaker and increase the frequency you'd also be increasing the speed of the sound wave, but that's not what happens. If you increase the frequency, the wavelength will decrease by that same factor, and the speed of the sound wave will remain the same. In fact, there's nothing you can do to the speaker that would increase the speed of sound. So, how can we change the speed of sound? Well, the only way to change the speed of sound is to change the medium or the properties of the medium that the sound wave is traveling in. So, to change the speed of sound in air, you can change things like the temperature of the air or the humidity of the air or the density of the air, or you can swap out the air entirely for another material, like water or helium or a metal. All of these changes to the medium would affect the speed of sound. People often think that changing the amplitude will change the speed of a sound wave, but it won't. If we create a sound pulse with a large amplitude, it won't travel any faster than a sound pulse with a small amplitude in the same medium. It will just be louder. In other words, yelling won't cause anyone to hear you faster, they'll just hear a louder sound when the sound wave arrives at their location. So remember, the speed of a sound wave is determined entirely by the properties of the medium through which it's traveling.