Editing Speed of sound (section)

==Effect of frequency and gas composition==

===General physical considerations===
The medium in which a sound wave is travelling does not always respond adiabatically, and as a result, the speed of sound can vary with frequency.<ref>[[Albert Beaumont Wood|A B Wood]], A Textbook of Sound (Bell, London, 1946)</ref>

The limitations of the concept of speed of sound due to extreme attenuation are also of concern. The attenuation which exists at sea level for high frequencies applies to successively lower frequencies as atmospheric pressure decreases, or as the [[mean free path]] increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes.<ref name="USSA1976"/> The standard equations for the speed of sound apply with reasonable accuracy only to situations in which the wavelength of the sound wave is considerably longer than the mean free path of molecules in a gas.

The molecular composition of the gas contributes both as the mass (M) of the molecules, and their heat capacities, and so both have an influence on speed of sound. In general, at the same molecular mass, monatomic gases have slightly higher speed of sound (over 9% higher) because they have a higher ''γ'' ({{nobreak|1=5/3 = 1.66}}...) than diatomics do ({{nobreak|1=7/5 = 1.4}}). Thus, at the same molecular mass, the speed of sound of a monatomic gas goes up by a factor of
<math display="block">{c_{\mathrm{gas,monatomic}} \over c_{\mathrm{gas,diatomic}}} = \sqrt{{{{5/3} \over {7/5}}}} = \sqrt{25 \over 21} = 1.091\ldots</math>

This gives the 9% difference, and would be a typical ratio for speeds of sound at room temperature in [[helium]] vs. [[deuterium]], each with a molecular weight of 4. Sound travels faster in helium than deuterium because adiabatic compression heats helium more since the helium molecules can store heat energy from compression only in translation, but not rotation. Thus helium molecules (monatomic molecules) travel faster in a sound wave and transmit sound faster. (Sound travels at about 70% of the mean molecular speed in gases; the figure is 75% in monatomic gases and 68% in diatomic gases).

In this example we have assumed that temperature is low enough that heat capacities are not influenced by molecular vibration (see [[heat capacity]]). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas give the gas additional ways to store heat which do not affect temperature, and thus do not affect molecular velocity and sound velocity. Thus, the effect of higher temperatures and vibrational heat capacity acts to increase the difference between the speed of sound in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.

===Practical application to air===
By far, the most important factor influencing the speed of sound in air is temperature. The speed is proportional to the square root of the absolute temperature, giving an increase of about {{val|0.6|u=m/s}} per degree Celsius. For this reason, the pitch of a musical wind instrument increases as its temperature increases.

The speed of sound is raised by humidity. The difference between 0% and 100% humidity is about {{val|1.5|u=m/s}} at standard pressure and temperature, but the size of the humidity effect increases dramatically with temperature.

The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about {{val|0.1|u=m/s}} as the frequency rises from {{val|10|u=Hz}} to {{val|100|u=Hz}}. For audible frequencies above {{val|100|u=Hz}} it is relatively constant. Standard values of the speed of sound are quoted in the limit of low frequencies, where the wavelength is large compared to the mean free path.<ref>{{cite web
| url = http://www.phy.mtu.edu/~suits/SpeedofSound.html
| title = Speed of Sound in Air
| publisher = Phy.mtu.edu
| access-date = 13 June 2014
| archive-date = 23 June 2017
| archive-url = https://web.archive.org/web/20170623092133/http://www.phy.mtu.edu/~suits/SpeedofSound.html
| url-status = dead
}}</ref>

As shown above, the approximate value 1000/3 = 333.33... m/s is exact a little below {{val|5|u=degC}} and is a good approximation for all "usual" outside temperatures (in temperate climates, at least), hence the usual rule of thumb to determine how far lightning has struck: count the seconds from the start of the lightning flash to the start of the corresponding roll of thunder and divide by 3: the result is the distance in kilometers to the nearest point of the lightning bolt.  Or divide the number of seconds by 5 for an approximate distance in miles.