Sound Waves

“Waves are the result of a disturbance of some sort-the motion of an object, a change in an electrical current, or an alteration of an electromagnetic field. The disturbance is transported from one point to another by a wave, but the medium through which it travels does not undergo a net displacement.” In simpler terms, a disturbance of particles in a medium (a substance through which something else is transmitted or carried on) causes a wave, which transports energy (the capacity to do work) without leaving the medium away from its original position. There are several basic properties of waves, shown below in the diagram of a standing wave.

The points on the diagram that are labeled “crest” are the highest points on the wave. The troughs are the lowest points. These points are measured in relation to their distance from the equilibrium (the amplitude.) In sound waves, amplitude is the measure of loudness. It is the maximum amount of displacement in a wave from its resting point (in this diagram, the dotted line.) It is the measure of how much energy a wave has. The crests and troughs of waves move either to the side or up and down and as a result, the troughs will become crests and the crests will become troughs. It is part of the wave cycle.

The wavelength is the distance between two crests or two troughs. It is the distance the wave has traveled during complete cycle. Wavelength is measured in meters because it is a distance. The diagram above shows one and a half wavelengths, because there are two crests (1 wavelength) and one trough (1/2 wavelength.) A wave with a wavelength of two would have two crests and two troughs. Nodes are the points on the wave that are standing still. There is no displacement on these points. The frequency of a wave is defined as how many cycles a wave completes in one second. One cycle means that a certain point on a wave returns to its starting point after forming one crest and one trough. A complete cycle is illustrated in the diagram below. Frequency is measured in hertz. One hertz equals one cycle per second.

Velocity is the distance an object travels in a specific direction during a period of time. It is different than “speed” because speed does not specify the direction of motion. There are two different categories of waves: longitudinal waves and transverse waves. Longitudinal waves are those in which the particles of the medium are put out of place in a direction that that is parallel to direction of the transportation of energy. Sound waves, the focus of this paper, are longitudinal waves. A slinky could be used to create an example of a longitudinal wave. Stretching it out horizontally on the floor and vibrating one end of it back and forth in a horizontal direction would create a longitudinal wave. In the slinky longitudinal wave, there are certain regions in the coils that become pressed together. There are other regions where the coils are spread apart. These areas are known as compressions and rarefactions, respectively. The slinky is moving longitudinally, and the sections that move in and out from the center are the crests and troughs. The amplitude would be measured from the peak of a crest or trough to the position the slinky would be in if it were not moving, (the equilibrium position.) The moving sections are the rarefactions; they are stretched out to the sides. Rarefactions are the points on waves with the least amount of density (“the ratio of the mass of a substance to its volume.” ) These points have the least amount of coils in a certain space. The compressions, however, have more coils packed together, because they are the nodes of the wave. They will not move from the line of equilibrium. Suppose a shoebox guitar was created (a shoebox with rubber bands around it.) The instrument would create longitudinal sound waves by vibrating the rubber bands. As the bands would flex in and out (from being plucked) the molecules of the medium would move in accordance to the flexing of the bands. The moving of the bands in the medium would create pressure changes. As the band flexed in, molecules would be sucked in, and when they flexed outward, molecules would be pushed out, creating a disturbance in the medium. When the rubber bands are plucked, the molecules all around move, and they in turn move the molecules around them. The vibration from the simple instrument is carried forward by these disturbances. ‘The frequency of this sound would be determined by the speed of the air pressure fluctuations. If the air pressure fluctuates back and forth more quickly, the frequency would be higher. This is known as a higher pitch. Fewer fluctuations in a period of time mean a lower pitch. The level of air pressure in each fluctuation, the wave’s amplitude determines how loud the sound is.’

A somewhat similar disturbance can be observed in a game of pool. The cue ball is shot towards the other balls, all set up and touching each other. When the cue hits the first ball, the tip of a triangle of balls, it forces that ball to move. That ball will then move forward and impact the other balls touching it. This process continues until all balls have been displaced. The difference, however, between this example and an actual sound wave is that the balls will not return to their original positions after moving. The cue ball is not constrained like a rubber band; it does not flex back. Therefore, the pressure remains the same, and all balls continue outward in an expanding direction. To get the full magnitude of the effects of a sound wave, sets of pool balls would have to be set up all around the cue so that the displacement occurs on all sides of the disturbance. The sound is carried by the disturbances in the position of the molecules and is received by the human ear. The sound waves travel through the medium and hit the eardrum. The eardrum then picks up the vibration and passes it along through the rest of the ear. When it vibrates, it hits the malleus, often called the hammer, and moves it side to side like lever. This little bone is connected to the incus (or anvil) which is attached to the stapes, or stirrup. The end of this little bone rests against the cochlea. When the air pressure from the wave pushes on the eardrum, the three little bones, the ossicles, move so that the end of the stapes pushes in on the fluid inside the cochlea. When the air pressure pulls out on the eardrum (a rarefaction) the ossicles move and the end of the stapes pulls in on the fluid. This process creates waves in the inner ear fluid. These waves are then received by the inner ear where it is translated into nerve impulses and sent to the brain to be read. To amplify a sound wave as to make it audible for someone in a nearby room, one could simply pluck harder on the string of the shoebox guitar. This would cause the strings to create larger pressure fluctuations. The sound wave would have a bigger amplitude and thus, a louder sound. The sound would travel farther than it normally would, allowing someone in a nearby room to hear the sound.