A pendulum is a suspended object that swings to and fro with regularity. a rock suspended at the end of a string is a pendulum. Gallileo discovered that the period of a pendulum, or the time it takes to complete one full to and fro vibration, depends only on the length of the pendulum and not on its mass. A long pendulum has a longer period than a short pendulum. The vibratory motion of a swinging pendulum is called simple harmonic motion. Springs also exhibit simple harmonic motion. Consider a spring with a pen at the bottom of it vibrating back and forth across a sheet of paper. The pen traces out a straight line. When the paper is being moved while the spring is vibrating, the spring will trace out a special curve called a sine curve. A sine curve is a pictorial representation of a wave. The high points of the sine curved are called crests. The low points are called troughs. A line through the middle of the wave represents the midpoint of vibration. The maximum distance the wave is from the midpoint of vibration, or the distance from the midpoint of vibration to the crest, is called amplitude. The wavelength is the distance between two successive crests or troughs, or the distance between any two successive parts of the wave. Wave length is not the distance between crest and trough.

The frequency of a vibration is how frequently the vibration occurs. It is the number of to and fro vibrations in a given time interval (usually one second). The unit of frequency is the hertz (Hz). One hertz is one vibration per second, two is two vibrations per second, etc. All waves are caused by vibrations. Vibrations in water cause water waves, vibration of air causes sound waves, vibration of electrons causes electromagnetic waves. The frequency of the vibrational source of the wave is the same as the frequency of the wave. To find the frequency of a wave, choose a point and count how many complete waves pass the point every second. Remember, the frequency of a wave is equal to the frequency of its vibrational source. Once a wave's frequency is known, its period can be calculated. If a wave has a frequency of two hertz, what is its period? How long does it take for one wave to pass by, if two waves pass by each second? 1/2 of a second! Period is the inverse of frequency, or P=1/f.

The speed of a wave is related to the frequency and wavelength of the wave. Consider water waves spreading out. Pick a point on the water's surface and observe the waves passing that point. You can measure how much time passes between crests-one period-and measure the distance between the crests-one wavelength. Speed=distance/time. When distance is the wavelength and time is the period, speed =wavelength/period. Remember that frequency is the inverse of period, so speed=wavelength times frequency.

Consider a slinky tied to a wall. Shake the slinky up and down, and waves will travel along the slinky toward the wall. The wave is travelling towards the wall, but the motion of the crests and troughs are up and down, at right angles to the direction the wave is travelling. A wave where the motion of the medium (crests and troughs) is at right angles to the motion of the wave is called a transverse wave. Now consider moving the slinky back and forth instead of up and down. Wave motion is still occurring. You will note periodic compressions, where the coils of the spring are close together, and rarefractions, where the coils of the spring are far apart, moving towards the wall. In this case the motion of the medium (compressions and rarefractions) is in the same direction as the motion of the wave. This type of wave is called a longitudinal wave.

More than one wave can share the same space. If we drop two rocks into the water, the waves formed by them will overlap and form an interference pattern. When more than one wave occupies the same area, the displacements of the waves will add at every point. When the crest of one wave overlaps the crest of another, their individual effects combine to produce a wave with a larger amplitude. This is called constructive interference. When the trough of one wave overlaps the crest of another, the individual effects are reduced, and the waves may even disappear completely. This is called destructive interference.

Consider a rope hung on a wall. If you shake one end of the rope, waves are formed in the rope. The waves travel to the wall and then reflect back. If the rope is vibrated with just the right frequency, a standing wave may be produced. A standing wave is a wave where certain points, called nodes, are stationary. These points always have zero amplitude. The points on the wave where amplitude is at a maximum are called anti-nodes. In a standing wave, the nodes never move and the anti-nodes switch from crest to trough to crest to trough, while appearing to stay in the same place. In other words, the wave does not appear to be moving towards the wall.

Consider a boat halfway between two channel markers. If the boat is put in neutral, it vibrates and sends out water waves. These waves will pass the first channel marker with the same frequency they pass the second channel marker. The waves will form concentric circles.

Now consider what happens if this same boat begins to move toward the first channel marker. The boat is "chasing" the waves it has already produced. The wave pattern is no longer concentric circles, and the frequency of the waves passing the channel markers are no longer the same. The frequency is greater at the first channel marker than at the second. This change in frequency due to the motion of a wave source is known as the Doppler effect. It can be easily seen on the street. When a car moves towards you, you hear the frequency, or the pitch, of the car's engine rise. As it passes you and moves away, the pitch and frequency is lower.

When the speed of our boat is the same as the speed of the waves it produces, the waves will pile up in front of the boat. The boat will be keeping up with the leading edge of each wave. When the boat moves faster than the waves it produces, it makes a v-shaped pattern of waves with overlapping edges. The boat moves in wave-free water. This same sort of a thing happens with planes moving faster than the speed of sound. The people in the plane do not hear the sound the plane produces, because they are moving ahead of it.

The wave-pattern that the boat produced when it moved faster than the waves it produces is called a bow-wave. An aircraft travelling faster than the speed of sound produces a wave-pattern called a shock wave. The shock wave is a conical shell of compressed air. When the shock wave passes a person on the ground, they hear a loud sound called a sonic boom. We don't hear a sonic boom from aircraft travelling slower than the speed of sound because the sound waves they produce reach our ears one by one. Sound waves from aircraft travelling faster than the speed of sound overlap and reach our ears in a single burst. It is not necessary for an object to be noisy to produce a sonic boom. A bullet produces no noise of its own at all, but if it passes over our heads we hear the crack of a sonic boom. A larger object would disturb more air and make a louder sound. If an object is moving faster than the speed of sound, it will make a sound, no matter how quiet it is.