# Sound Waves Interactive

With this simulator you can investigate how sound waves travel through the air. When you become experienced with this simulator and the physical principles behind the program, you can use a sleek version which loads faster on-line and does not include these instructions.

## Speed of a Sound

As any object moves through the air, the air near the object is disturbed. Small disturbances are transmitted through the air at a distinct speed called the speed of sound. Sound is just a sensation created in the human brain in response to small pressure fluctuations in the air. The transmission of a small disturbance through a gas is an isentropic process. The conditions in the gas are the same before and after the disturbance passes through.

## Series of Waves

In our simulation, a bug is creating a sound which moves through the air as a series of waves. When the waves pass our microphone, the sound is detected. The distance between any two waves is called the wavelength and the time interval between waves passing is called the period. The inverse of the period is the frequency of the wave. which is measured in cycles/second. The brain associates a certain musical pitch with each frequency; the higher the frequency, the higher the pitch. Likewise, shorter wavelengths produce higher pitches since more waves pass through a point every second. The speed of transmission of the sound remains a constant regardless of the frequency or the wavelength since the speed only depends on the state of the air not on the characteristics of the generating source.

## General Instructions

While the speed of sound does not change, the speed of the source of the sound is arbitrary. You can change the speed of the bug by using the slider at the bottom. You can start or stop the motion of the bug by using the appropriate buttons. If the source is stopped, you can advance or retreat by a single time increment by using the “Step Forward” and “Step Back” buttons. And you can “Resume” the animation by pushing that button. Notice how the frequency of the sound changes when the source is moving and notice how the waves collect into a Mach wave when the object moves faster than Mach 1.0, the speed of sound.

## Physics of the Speed of Sound Waves

Here are some of the interesting physics problems which you will observe with this simulator. If the source moves slower than the speed of sound, conditions are said to be subsonic. As the source moves it continues to generate sound waves which move at the speed of sound. Since the source is moving slower than the speed of sound, the waves move out away from the source. Upstream (in the direction of the motion), the waves bunch up and the wavelength decreases. Downstream, the waves spread out and the wavelength increases. The sound that our microphone detects will change in pitch as the object passes. This change in pitch is called a doppler effect. If the source moves at or near the speed of sound conditions are said to be sonic or transonic. In this case, the waves again bunch up upstream and spread out downstream. But because the source speed is nearly the sound speed, the upstream wavelength becomes nearly zero and the individual waves collect into a single Mach wave. If the source moves higher than the speed of sound conditions are said to be supersonic. The Mach wave now becomes conical and the angle of the cone depends on the ratio of the speed of sound to the speed of the object; the faster the speed of the object the sharper (smaller) the cone angle. The ratio of the object speed to the speed of sound is the Mach number of the flow, which explains the name “Mach wave”.

## Shock Waves

We must be very careful not to confuse the Mach waves which appear in this simulation with shock waves that occur in supersonic flows. In this simulation, we have only considered the isentropic transmission of the sound generated by the bug. We haven’t looked at how the flow gets around the bug itself. The motion of the gas around the bug generates shock waves which are not isentropic. Shock waves in the flow are not inclined at the Mach angle but at a different angle which depends on the shape and speed of the bug. The Mach angle is determined by conditions in the flow.

Please note: the simulation below is best viewed on a desktop computer. It may take a few minutes for the simulation to load.

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