Question

In: Physics

a) What is the equation of motion that governs the physics behind sound production in your...

a) What is the equation of motion that governs the physics behind sound production in your speaker? Discuss what each term in this equation of motion relates to in your speaker.

Solutions

Expert Solution

Wave interference is the phenomenon that occurs when two waves meet while travelling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium.

If two upward displaced pulses having the same shape meet up with one another while travelling in opposite directions along a medium, the medium will take on the shape of an upward displaced pulse with twice the amplitude of the two interfering pulses. This type of interference is known as constructive interference.

If an upward displaced pulse and a downward displaced pulse having the same shape meet up with one another while travelling in opposite directions along a medium, the two pulses will cancel each other's effect upon the displacement of the medium and the medium will assume the equilibrium position. This type of interference is known as destructive interference.

Sound is a pressure wave that consists of compression and rarefaction. As a compression passes through a section of a medium, it tends to pull particles together into a small region of space, thus creating a high-pressure region. And as a rarefaction passes through a section of a medium, it tends to push particles apart, thus creating a low-pressure region. The interference of sound waves causes the particles of the medium to behave in a manner that reflects the net effect of the two individual waves upon the particles.

For example, if a compression (high pressure) of one wave meets up with a compression (high pressure) of a second wave at the same location in the medium, then the net effect is that that particular location will experience an even greater pressure. This is a form of constructive interference. If two rarefaction (two low-pressure disturbances) from two different sound waves meet up at the same location, then the net effect is that that particular location will experience an even lower pressure. This is also an example of constructive interference.

Two Source Sound Interference

A popular Physics demonstration involves the interference of two sound waves from two speakers. The speakers are set approximately 1-meter apart and produced identical tones. The two sound waves traveled through the air in front of the speakers, spreading out through the room in spherical fashion. A snapshot in time of the appearance of these waves is shown in the diagram below. In the diagram, the compression of a wavefront are represented by a thick line and the rarefaction are represented by thin lines. These two waves interfere in such a manner as to produce locations of some loud sounds and other locations of no sound. Of course the loud sounds are heard at locations where compression meet compression or rarefaction meet rarefaction and the "no sound" locations appear wherever the compression of one of the waves meet the rarefaction of the other wave. If you were to plug one ear and turn the other ear towards the place of the speakers and then slowly walk across the room parallel to the plane of the speakers, then you would encounter an amazing phenomenon. You would alternatively hear loud sounds as you approached anti-nodal locations and virtually no sound as you approached nodal locations. (As would commonly be observed, the nodal locations are not true nodal locations due to reflections of sound waves off the walls. These reflections tend to fill the entire room with reflected sound. Even though the sound waves that reach the nodal locations directly from the speakers destructively interfere, other waves reflecting off the walls tend to reach that same location to produce a pressure disturbance).

Destructive interference of sound waves becomes an important issue in the design of concert halls and auditoriums. The rooms must be designed in such as way as to reduce the amount of destructive interference. Interference can occur as the result of sound from two speakers meeting at the same location as well as the result of sound from a speaker meeting with sound reflected off the walls and ceilings. If the sound arrives at a given location such that compressions meet rarefactions, then destructive interference will occur resulting in a reduction in the loudness of the sound at that location. One means of reducing the severity of destructive interference is by the design of walls, ceilings, and baffles that serve to absorb sound rather than reflect it.

The destructive interference of sound waves can also be used advantageously in noise reduction systems. Earphones have been produced that can be used by factory and construction workers to reduce the noise levels on their jobs. Such earphones capture sound from the environment and use computer technology to produce a second sound wave that one-half cycle out of phase. The combination of these two sound waves within the headset will result in destructive interference and thus reduce a worker's exposure to loud noise.


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