Most sounds are produced by the vibrations of material objects. In a guitar, the string vibrates. This in turn vibrates the air, forming a longitudinal air wave with compressions and rarefactions of the air molecules. The frequency of the wave is the same as the frequency of the string. We describe our perception of the frequency of a sound wave by the word pitch. A high pitch corresponds with a high frequency. The human ear can only hear sounds with frequencies between twenty and twenty thousand Hz. We cannot hear infrasonic waves, which have frequencies lower than twenty Hz, or ultrasonic waves, which have higher frequencies than twenty thousand Hz.
The sounds that we mostly hear travel through the air. However, any elastic substance can transmit sound. In liquids and solids, sound travels about four times faster than in air. This is because the molecules of these materials are close to each other, and transmit the compressions and rarefractions without much loss of energy. This greater speed can be demonstrated on the street. Put your ear on the ground by a road until you hear a car coming. Then lift your ear up. You will not be able to heart he car.
Thunder is heard after lightning is seen. This example illustrates that sound takes a recognizable amount of time to travel from one point to another. The speed of sound in air depends on factors such as wind, temperature, and humidity. It does not depend on the loudness or the frequency of the sound. Sound traveling in air at room temperature has a speed of about 340 m/s. Sound can be reflected. The reflection of sound is called an echo. When sound is reflected, some of the sound's energy is absorbed. The fraction of energy carried by the reflected sound wave is largest when the reflecting surface is rigid and smooth, and smallest when the surface is soft and irregular. When sound reflects of a substance, the angle of incidence is the same as the angle of reflection. This means that sound bounces off a wall at the same angle that it hits the wall. When multiple reflections of sound, or reverberations, occur, the sound waves may interfere with each other, causing the sound to be garbled.
Sound waves bend when parts of the wave fronts travel at different speeds. This occurs when sound travels in an area of uneven temperature. Hot air molecules move faster, and therefore transmit sound energy faster. So sound has a higher speed in hot air. When part of a sound wave is travelling through hot air, and another part is travelling through cool air, the part travelling through the hot air will move faster. This will cause it to get ahead of the cool air portion and bend towards the cold air. This bending of sound is called refraction.
Sound waves contain relatively little energy. When sound travels through the air, this energy begins to turn into thermal energy, quickly dissipating the sound. High frequencies of sound lose their energy faster than low frequencies of sound.
Every two objects vibrate differently when they are struck. Any object made of an elastic material will vibrate at its own special frequency when struck. This frequency is called the object's natural frequency. Most atoms and objects are at least somewhat elastic, so most objects have their own natural frequency. If one object is made to vibrate and then placed on another object, the second object will begin to vibrate. This is called a forced vibration. When the frequency of forced vibrations on an object matches the object's natural frequency, a large increase in the amplitude of the forced vibration occurs. This is called resonance. Consider two tuning forks with the same frequency. When one is struck, it sets off compressions and rarefactions of air, forming areas of high pressure and low pressure. When the compression strikes the second fork, it pushes the prongs forward. Because they are elastic, they spring back. Because they move backwards into a low pressure area, caused by the rarefaction, they spring back too far and then have to move forward. At this point, a second compression of air strikes them, pushing them even further forward. The second tuning fork starts to vibrate. Two tuning forks with different frequencies would not resonate, because the timing of the compressions and rarefractions would be off. A microwave oven works because the oven sets off microwaves, which closely match the natural frequency of the molecules in most foods. The food molecules resonate, and heat up.
Consider two tuning forks of slightly different frequencies. If they are both struck, the sound waves produced by them will interfere with each other. Sometimes the waves will be "instep" with each other, and sometimes the waves will be "out of step" with each other. At instep areas, the waves will interfere constructively. At out of step areas, the waves will interfere destructively. Loud sounds will be heard at constructive areas, and soft sounds will be heard at destructive areas. We will hear an alternation of loud and soft sounds called a beat. The frequency of a beat, or how often we hear the change from loudness to softness, is equal to the difference in frequency between the two vibrating objects. A 400 Hz object and a 399 Hz object will produce a beat frequency of 1 Hz.
The pitch of a sound relates to its frequency. Most sounds are composed of many frequencies, and in these sounds pitch corresponds to the lowest frequency. Different musical notes can be made from an instrument by changing the size, tension, or mass of the vibrating object. The intensity of sound depends on the amplitude of the sound waves. Amplitude in a longitudinal wave corresponds to the difference between the high and low pressure area of the wave. Intensity is measured in watts/meters squared. We usually use a different, logarithmic scale to measure sound, called the decibel (dB) scale. A sound at 10-12 w/m2 corresponds to zero dB, a sound at 10-11 w/m2 corresponds to ten decibels, etc. A sound of ten decibels is ten times greater than a sound of zero decibels. A sound of twenty decibels is one hundred times greater than a sound of zero decibels.
Most musical sounds are formed by a combination of many tones. The various tones are called partial tones. The tone that determines the pitch, the one with the lowest frequency, is called the fundamental frequency. Partial tones that have frequencies that are whole number multiples of the fundamental frequency are called harmonics.
A French mathematician, Joseph Fourier, discovered a mathematical regularity to the various components of wave motion. He discovered that even the most complex waves are composed of simple sine waves that add together. He discovered a mathematical operation for breaking down waves into their component sine waves, called Fourier analysis.
