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Check Also. Sound and Oscillation. What are some Applications of Doppler Effect? February 3, Facebook Twitter WhatsApp Telegram. Doppler effect. Types of electromagnetic waves. Difference between mechanical and matter waves. Why are we interested in the speed of sound? The speed of "sound" is actually the speed of transmission of a small disturbance through a medium. Sound itself is a sensation created in the human brain in response to sensory inputs from the inner ear.
We won't comment on the old "tree falling in a forest" discussion! Disturbances are transmitted through a gas as a result of collisions between the randomly moving molecules in the gas. Since temperature and thus the speed of sound decreases with increasing altitude up to 11 km , sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. However, there are variations in this trend above 11 km.
In particular, in the stratosphere above about 20 km , the speed of sound increases with height, due to an increase in temperature from heating within the ozone layer. This produces a positive speed of sound gradient in this region.
Still another region of positive gradient occurs at very high altitudes, in the aptly-named thermosphere above 90 km. This equation is derived from the first two terms of the Taylor expansion of the following more accurate equation:. The value of This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and for this reason will fail, particularly at higher temperatures.
It gives good predictions in relatively dry, cold, low-pressure conditions, such as the Earth's stratosphere. The equation fails at extremely low pressures and short wavelengths, due to dependence on the assumption that the wavelength of the sound in the gas is much longer than the average mean free path between gas molecule collisions. A derivation of these equations will be given in the following section. A graph comparing results of the two equations is at right, using the slightly different value of For an ideal gas, K the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids is given by.
This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for c air have been found to vary slightly from experimentally determined values. Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic.
Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities for air, this includes standard Earth sea-level conditions. For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature see tables below. See the section on gases in specific heat capacity for a more complete discussion of this phenomenon. Then, for dry air,. The above derivation includes the first two equations given in the "Practical formula for dry air" section above.
The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. This will increase the audibility of sounds downwind.
This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind. For sound propagation, the exponential variation of wind speed with height can be defined as follows: . In the American Civil War Battle of Iuka , an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle,  because they could not hear the sounds of battle only 10 km six miles downwind. In the standard atmosphere :.
In fact, assuming an ideal gas , the speed of sound c depends on temperature only, not on the pressure or density since these change in lockstep for a given temperature and cancel out.
Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere— actual conditions may vary. Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:. 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.
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. 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. Thus, at the same molecular mass, the speed of sound of a monatomic gas goes up by a factor of.
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. Note that 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. 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 0. For this reason, the pitch of a musical wind instrument increases as its temperature increases.
The speed of sound is raised by humidity but decreased by carbon dioxide. The carbon dioxide content of air is not fixed, due to both carbon pollution and human breath e. The dependence on frequency and pressure are normally insignificant in practical applications. In dry air, the speed of sound increases by about 0.
For audible frequencies above 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. Mach number, a useful quantity in aerodynamics, is the ratio of air speed to the local speed of sound. At altitude, for reasons explained, Mach number is a function of temperature. Aircraft flight instruments , however, operate using pressure differential to compute Mach number, not temperature.
The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the stagnation pressure sensed by a Pitot tube is dependent on altitude as well as speed.
The earliest reasonably accurate estimate of the speed of sound in air was made by William Derham and acknowledged by Isaac Newton. On a calm day, a synchronized pocket watch would be given to an assistant who would fire a shotgun at a pre-determined time from a conspicuous point some miles away, across the countryside.Oct 17, · Here is a plot of the speed of sound at different heights above sea level. At sea level, the value is right around the m/s mark. If you move up to , feet, the speed will drop down to.