The speed of a sound wave in air depends upon the properties of the air, namely the temperature and the pressure. The pressure of air (like any gas) will effect the mass density of the air (an inertial property) and the temperature will effect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through air is approximated by the following equation:
v = 331 m/s +
(0.6 m/s/C)*T
where T is the temperature of the air in degrees Celsius. Using this equation is used to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.
v = 331 m/s + (0.6 m/s/C)*20 C
v = 331 m/s + 12 m/s
v = 343 m/s
At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of
If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.
Another phenomenon related to the perception of time delays between two events is the phenomenon of echolation. A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. If you have ever made a holler within a canyon, perhaps you have heard an echo of your holler off a distant canyon wall. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the canyon wall. For instance if an echo is heard 2.2 seconds after making the holler, then the distance to the canyon wall can be found as follows:
The canyon wall is 380 meters away. You might have noticed that the time of 1.1 seconds is used in the equation. Since the time delay corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back, the one-way distance to the canyon wall corresponds to one-half the time delay.
While the phenomenon of echolation is of relatively minimal importance to humans, it is an essential trick of the trade for bats. Being merely blind, bats must use sound waves to navigate and hunt. They produce short bursts of ultrasonic sound waves which reflect off their surroundings and return. Their detection of the time delay between the sending and receiving of the pulses allows a bat to approximate the distance to surrounding objects. Some bats, known as Doppler bats, are capable of detecting the speed and direction of any moving objects by monitoring the changes in frequency of the reflected pulses.
Like any wave, a sound wave has a speed which is mathematically related to the frequency and the wavelength of the wave. The mathematical relationship between speed, frequency and wavelength is given be the following equation.
Speed =
Wavelength * Frequency
Using the symbols v,
,
and f, the equation can be re-written as
v = f * 
The above equations are useful for solving mathematical problems related to the speed, frequency and wavelength relationship. However, one important misconception could be conveyed by the equation. Even though wave speed is calculated using the frequency and the wavelength, the wave speed is not dependent upon these quantities. An alteration in wavelength does not effect (i.e., change) wave speed. Rather, an alteration in wavelength effects the frequency in an inverse manner. A doubling of the wavelength results in a halving of the frequency; yet the wave speed is not changed. The speed of a sound wave depends on the properties of the medium through which it moves and the only way to change the speed is to change the properties of the medium.
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