Wind Gradient - Sound Propagation

Sound Propagation

Wind gradient can have a pronounced effect upon sound propagation in the lower atmosphere. This effect is important in understanding sound propagation from distant sources, such as foghorns, thunder, sonic booms, gunshots or other phenomena like mistpouffers. It is also important in studying noise pollution, for example from roadway noise and aircraft noise, and must be considered in the design of noise barriers. When wind speed increases with altitude, wind blowing towards the listener from the source will refract sound waves downwards, resulting in increased noise levels behind the barrier. These effects were first quantified in the field of highway engineering to address variations of noise barrier efficacy in the 1960s.

When the sun warms the Earth's surface, there is a negative temperature gradient in atmosphere. The speed of sound decreases with decreasing temperature, so this also creates a negative sound speed gradient. The sound wave front travels faster near the ground, so the sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source. The radius of curvature of the sound path is inversely proportional to the velocity gradient.

A wind speed gradient of 4 (m/s)/km can produce refraction equal to a typical temperature lapse rate of 7.5 °C/km. Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, eliminating the acoustic shadow on the downwind side. 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.

There will usually be both a wind gradient and a temperature gradient. In that case, the effects of both might add together or subtract depending on the situation and the location of the observer. The wind gradient and the temperature gradient can also have complex interactions. For example, a foghorn can be audible at a place near the source, and a distant place, but not in a sound shadow between them. In the case of transverse sound propagation, wind gradients do not sensibly modify sound propegation relative to the windless condition; the gradient effect appears to be important only in upwind and downwind configurations.

For sound propagation, the exponential variation of wind speed with height can be defined as follows:

where:

= speed of the wind at height, and is a constant

= exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52

= expected wind gradient at height

In the 1862 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 six miles downwind.

Scientists have understood the effect of wind gradient upon refraction of sound since the mid 1900s; however, with the advent of the U.S. Noise Control Act, the application of this refractive phenomena became applied widely beginning in the early 1970s, chiefly in the application to noise propagation from highways and resultant design of transportation facilities.