How we perceive sound
To better understand the manner in which a sound wave travels, think of a point source of sound. Like light, a point source of sound emits sound rays in all directions, in an ever growing sphere from the source. As the sphere gets bigger, its surface is farther from the point source, while the same amount of sound energy is distributed over a larger area and thus the intensity of the sound decreases. This is the reason that sounds grow fainter at greater distances. Intuitively we can see that the larger the amplitude of the sound wave, the greater loudness of the sound and the greater the intensity. The square of the amplitude of the wave is directly proportional to the intensity of the sound. Imagine strumming a chord on a guitar. The harder you pluck, the more the string moves from its equilibrium position and thus the greater the amplitude of the wave, and the louder the note sounded. It is difficult to measure this amplitude, but it is not that difficult to measure the intensity. The intensity of a sound wave is the energy per unite time that it is transported by the wave, per unit area of wave front. In metric units, the unit of intensity is Watts (Joules per second) per meter squared, written symbolically as . However, sound is usually measured in intensity level rather than intensity. Intensity level is expressed on a logarithmic scale measured in decibels (dB), which is a scale designed to match our own subjective views of the loudness of sound. The difference, thus, between intensity and intensity level is that one is absolute while the other is adjusted for our human perception of loudness. In order to find intensity level in decibels, we begin with a reference intensity of which corresponds to 0 dB and is the lowest intensity that can be heard by the human ear. As it is a logarithmic scale, something 10 times as loud has an intensity of 10 decibels, while something 100 times as loud would have an intensity of 20 decibels. A more direct way of finding the intensity in dB of something given the intensity in is to use the following equation:
This is illustrated by the flash demonstration found here. The darkness of the line represents the intensity of the sound at that distance from the source.
As a quick reference, here are the intensity levels and intensities of a few common sounds:
Frequency and Pitch
As the frequency of a sound wave increases, we perceive the pitch to rise. In other words, a sound wave with a high frequency sounds like a higer note to us. Conversely, when the frequency of the wave decreases, we perceive the pitch to decrease. For example, the note middle C has a frequency around 261 Hz (Hz signifies cycles per second) while the note E, slightly higher up on the scale has a higher frequency of around 330 Hz. To be heard by humans a vibrating object must have a frequency ranging from about 20 Hz to 20,000 Hz. This is called the audio frequency or audibility range. Vibrations below the lower limit of the audibility ranger are known as infrasonic, while those above the upper limit are known as ultrasonic (not to be confused with supersonic which designates velocities faster than the speed of sound).
The Doppler Effect
Even if you have never heard of the Doppler effect, you have probably experienced it in your life. The Doppler effect occurs when there is relative motion between the source of sound or the observer and the medium through which the sound wave is propagating. It is named for a 19th century physicist, Christian Johann Doppler. Simply put, the frequency of the sound increases relative to a stationary observer as the source of sound approaches, and decreases as it moves away. The effect also occurs when a moving observer approaches or retreats from a stationary source. This is because as the observer or source move, the effective wavelength changes. As the observer approaches the source, or the source approaches the observer, the wavelength decreases, and since the speed of sound remains constant more wavefronts from the source hit the observer in a given period of time, so the frequency increases. The phenomenon is not unique to sound waves, but is most commonly noted in sound waves because the change in observed frequency results in a changing pitch, giving an easy way for people to hear when the Doppler effect is taking place. The change in pitch of a car horn as the car passes a stationary observer is an everyday example of the Doppler effect.
Click here for a java applet demonstrating the doppler effect.
Click here for a flash demo that shows this effect.
The following equations are all used to find the frequency that an observer notes when there is relative motion between the observer and the source of the sound: