A BRIEF INTRODUCTION TO THE PROPERTIES OF SOUND WAVES
By Lex Marburger
Excerpt - Page 1Contrary to what one’s eyes might tell them from looking at an oscilloscope, sound waves are not transverse; that is to say, they do not look like wiggling bits of string. Rather, sound waves are longitudinal, like a stretched spring when one end is pushed towards the other. Parts of the spring bunch up against other parts, and the force is continued on down the length of the spring until it reaches the end, upon where it bounces back. If one pictures the molecules in the air as the spring, sound waves would be the varying patterns of compression and rarefaction as they reach the end of the spring (i.e. one’s ear).
That much said, there is only a very small range of vibration that we call “sound”. In a perfect environment, a healthy human ear can hear a range of approximately 20 vibrations per second to 20,000. Typically, the terminology for “vibrations per second” is known as “Hertz”, or “Hz”. So, we can say that frequencies of 20 Hz to 20 KHZ (that is, 20 Hertz to 20 KiloHertz) are perceived as sound to the human ear. Any frequency below 20 Hz is known as “subsonic”, while any above 20 KHz is known as “supersonic” or “ultrasonic”. As an example, the lowest note on a grand piano is 27.50 Hz, while the lowest note on the electric bass is 41.2 Hz. Conversely, the highest note on a grand piano is 4435 Hz; frequencies above that are typically perceived as “color”, or harmonics, and are the “shimmering” sounds heard in cymbal crashes and other percussive sounds.
One may wonder why the piano, with 88 keys and over 7 octaves, can only reach the neighborhood of 4500 Hz (4.5 KHz). This is because the human ear hears frequencies in a non-linear manner. That is to say, a doubling of frequency is heard as a musical octave. For example, while the lowest note of a piano (known as “A0”) is 27.50 Hz, the frequency for A1 is 55 Hz, A2 is 110 Hz, and A3 is 220 Hz. In other words, while there is a difference of 27.5 Hz between notes is one particular octave, there is a difference of 110 Hz between another! Thought of in this way, it is quickly understood that there are only about two octaves above the highest note on a piano that we can hear.
In addition, the “length” of a sound wave can be defined, in reference to the “spring” analogy, as the distance between the maximum points of either compression or rarefaction along the spring (on an oscilloscope, the length is measured as between where the plotted sound wave crosses the X axis during a full “cycle”, that is the wave plotted both above and below said axis). Lower pitched sounds have longer waves, while higher pitched sounds have shorter wavelengths. The formula for finding wavelength is fairly simple:
λ = V/ƒ
Where λ is the wavelength, V is its velocity, and ƒ is the frequency. Because in this case V represents the speed of sound, it is generally thought of as a constant, 344 m/sec. However, certain factors can indeed change this speed, such as humidity and temperature. It should also be kept in mind that this is the speed of sound in air. The speed of sound increases as the density of the medium increases (e.g. the V of water is greater than that of air, and the V of steel is greater than water). As a side note, this is why in an ideal acoustical space, large stereo speakers should be suspended rather than placed on the floor, since the sound waves will travel quicker through the floor, leading to signal cancellation when combined with the slightly later arrival of the sound waves in the air.
