The speed of sound in room temperature air is 343.7 m/s. That corresponds to 1,128 ft/s or 769 miles/h.
In fact, the speed of sound depends on air temperature. The higher the tempera- ture, the faster the sound. The dependence is not a very strong dependence. A simple formula that can be used over the range of temperatures that we normally encounter gives the speed of sound as
vD331:7C0:6 TC; (5.1)
5.2 The Speed of Sound 43 where v is the speed of sound in meters per second andTC is the temperature in Celsius degrees. On the Celsius scale, room temperature is 20ı, and that is how we get the speed of sound to be 343.7 m/s at room temperature.
Interestingly, the speed of sound does not depend on the air pressure. On a clear day, when the barometer reads high or on a stormy day when the barometer reads low, the speed of sound is the same. The reason is that the effect of changing air pressure leads to mutually compensating changes in the air. Increasing the air pressure increases the elasticity of air, and this tends to increase the speed of sound.
But increasing the air pressure also increases the density of the air, and this tends to decrease the speed of sound. In the end, these two changes in the properties of air cancel one another.
5.2.1 Supersonic Things
Something that is supersonic goes faster than the speed of sound. Some airplanes are supersonic, and their speed is measured in Mach number, which is just a way of saying how many times faster than the speed of sound. For instance, the F16 fighter plane flies at Mach 2, which means twice the speed of sound (this was also the cruising speed of the Concorde passenger plane). Because the speed of sound is 769 miles per hour, you might conclude that the F16 flies at 1,538 miles per hour. That would be close but not quite right. The trick here is that the F16 flies at 50,000 ft.
At this high altitude the air is cold, and the speed of sound is only 670 miles per hour. Mach numbers are measured with respect to the ambient air. Therefore, for this plane, Mach 2 is only 1,340 mph.
A supersonic thing makes a shock wave that trails behind it so long as it continues to travel at supersonic speeds. For an aircraft traveling faster than Mach 1 this shock wave is called a sonic boom. It can break windows all along the path below the plane for as long as the plane flies supersonically.
Linearizing a Function
Equation (5.1) for the speed of sound is good and it is bad. It is good because it provides a simple way to calculate the speed of sound for any normal air temperature. It is simple because it is linear in the air temperature, TC. However, the equation is bad because it misrepresents the true way that the speed of sound actually depends on temperature. In reality, the speed of sound depends on the square root of the absolute temperature, referenced to absolute zero (273ıC). That dependence is shown in Fig.5.5 for temperatures ranging from194toC300ıC. It is not linear, it is curved.
The shaded region in Fig.5.5extends from18to 40ıC, corresponding to Fahrenheit temperatures from 0 to 104ı. That is the temperature range where we normally live. Over that small temperature range a straight line (linear) is a good approximation to the curve. Equation (5.1) represents that
44 5 Sound Waves
straight line approximation to the curve. It is an example of a mathematical technique commonly used in engineering and economics, linearizing a more complicated function to represent behavior over a limited range.
Fig. 5.5 The speed of sound depends on the square root of the absolute temperature, as shown by the heavy line, but over a restricted temperature range it is well represented by a straight line. (The asterisk at194ıshows where air becomes a liquid.) The shaded region indicates the normal range of outdoor air temperatures
5.2.2 Sound vs Light
Sound and light are both wave phenomena. However, there are enormous differences between sound waves and light waves. Most important, sound waves require a medium, such as air or water, to propagate. Light waves do not require a medium.
Light waves can travel through a vacuum. That is why we can see the sun (visible light) and feel its warmth (infrared light) but we cannot hear the sun.
Sound waves consist of pressure changes in the medium; light waves, including radio waves, consist of changes in an electromagnetic field. Light waves travel at the speed of light (How about that!). The speed of light is3108m/s. To compare that with the speed of sound in air, consider that 344 m/s is about3102m/s. Evidently light is faster by a factor of106, i.e., it is a million times faster. In the time that it takes a sound wave to go 40 m (130 ft) a light wave can go completely around the earth at the equator (25,000 miles). In the time that it takes sound to go 1 km, a light wave can travel to the Moon and back.
5.3 Sound Waves in Space and Time 45