We already had an basic approach on sound and sound waves in this article: Sound Waves. Now we will extend this approach into more details, in order to understand the basic sound theory and the basic functionality of our sound detector, the ear. Our ears are incredibly awesome receptors for sound waves. The threshold of hearing is somewhere around 1x10^-12 W/m^2. At this smallest of perceptible sound intensities, the eardrum vibrates less distance than the diameter of a hydrogen atom! Well, it's so small an amount of power that you can hardly conceive of it, but if you have pretty good hearing, you could detect a sound wave with that small amount of power. That's not all. You could also detect a sound wave a thousand times more powerful, a million times more powerful, and even a billion times more powerful. And, that's before it even starts to get painful!
Types of Sound Waves
Waves come in two basic types, depending on their type of vibration. Imagine laying a long slinky on the ground and shaking it back and forth. You would make what is called a transverse wave (see Picture 1 (a)). A transverse wave is one in which the medium vibrates at right angles to the direction the energy moves. If instead, you pushed forward and pulled backward on the slinky you would make a compressional wave (see Picture 1 (b)). Compressional waves are also known as longitudinal waves. A compressional wave is one in which the medium vibrates in the same direction as the movement of energy in the wave.
Picture 1: Transverse and Longitudinal (compressional) wave
If we take a snapshot of one transverse wave from the ceiling, it would look like Picture 2.
Picture 2: Wave elements
CREST: The topmost point of the wave medium or greatest positive distance from the rest position.
TROUGH: The bottom most point of the wave medium or greatest negative distance from the rest position.
WAVELENGTH (λ): The distance from crest to adjacent crest or from trough to adjacent trough or from any point on the wave medium to the adjacent corresponding point on the wave medium.
AMPLITUDE (A): The distance from the rest position to either the crest or the trough. The amplitude is related to the energy of the wave. As the energy grows, so does the amplitude. This makes sense if you think about making a more energetic slinky wave. You’d have to swing it with more intensity, generating larger amplitudes. The relationship is not linear though. The energy is actually proportional to the square of the amplitude. So a wave with amplitude twice as large actually has four times more energy and one with amplitude three times larger actually has nine times more energy.
FREQUENCY (f): The number of wavelengths to pass a point per second. In this case the frequency would be 3 per second. Wave frequency is often spoken of as “waves per second,” “pulses per second,” or “cycles per second.” However, the SI unit for frequency is the Hertz (Hz). 1 Hz = 1 per second, so in the case of this illustration, f = 3 Hz.
PERIOD (T): The time it takes for one full wavelength to pass a certain point. If you see three wavelengths pass your foot every second, then the time for each wavelength to pass is 1/3 of a second. Period and frequency are reciprocals of each other:
T = 1/f
f = 1/T
SPEED (v): Average speed is always a ratio of distance to time, v = d /t . In the case of wave speed, an appropriate distance would be wavelength, λ. The corresponding time would then have to be the period, T. So the wave speed becomes:
v = λ/T
v = λf
Sound Waves
If a tree falls in the forest and there’s no one there to hear it, does it make a sound? It’s a common question that usually evokes a philosophical response. I could argue yes or no convincingly. You will too later on. Most people have a very strong opinion one way or the other. The problem is that their opinion is usually not based on a clear understanding of what sound is.
One of the easiest ways to understand sound is to look at something that has a simple mechanism for making sound. Think about how a tuning fork makes sound. Striking one of the forks causes you to immediately hear a tone. The tuning fork begins to act somewhat like a playground swing. The playground swing, the tuning fork, and most physical systems will act to restore themselves if they are stressed from their natural state. The “natural state” for the swing, is to hang straight down. If you push it or pull it and then let go, it moves back towards the position of hanging straight down. However, since it’s moving when it reaches that point, it actually overshoots and, in effect, stresses itself. This causes another attempt to restore itself and the movement continues back and forth until friction and air resistance have removed all the original energy of the push or pull. The same is true for the tuning fork. It’s just that the movement (amplitude) is so much smaller that you can’t visibly see it. But if you touched the fork you could feel it. Indeed, every time the fork moves back and forth it smacks the air in its way. That smack creates a small compression of air molecules that travels from that point as a compressional wave. When it reaches your ear, it vibrates your eardrum with the same frequency as the frequency of the motion of the tuning fork. You mentally process this vibration as a specific tone.
Picture 3: The front of a speaker cone faces upward with several pieces of orange paper lying on top of it
A sound wave is nothing more than a compressional wave caused by vibrations. Next time you have a chance, gently feel the surface of a speaker cone (see Picture 3). The vibrations you feel with your fingers are the same vibrations disturbing the air. These vibrations eventually relay to your ears the message that is being broadcast. So, if a tree falls in the forest and there’s no one there to hear it, does it make a sound? Well … yes, it will certainly cause vibrations in the air and ground when it strikes the ground. And … no, if there’s no one there to mentally translate the vibrations into tones, then there can be no true sound. You decide. Maybe it is a philosophical question after all.
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