Activity 1
Making Waves
Background Information
Waves are a collective phenomena. The neighboring parts of the wave medium—the matter the wave moves through—interact and propagate a disturbance from one place to another. For spring waves, each part of the spring influences the neighboring parts through the force of the stretched spring. A disturbance in one part of the spring creates forces on neighboring parts, and the disturbance moves. The disturbance is a stretching of the spring from its equilibrium position, which is a straight spring. In Activity 1, the students disturb this equilibrium by whipping one end of spring back and forth to make a pulse, as shown in the drawing on page 185 of the Student Book.
In the pulse, the spring coils are stretched. This stretching exerts forces on these coils and pulls them back toward the equilibrium position. The stretching also puts forces on the nearby parts of the spring. These forces are reaction forces. When part of the spring is pulled one way, these reaction forces pull adjacent parts the other way. That is how the pulse moves.
Notice that the spring does not have to be motionless to be in the equilibrium position. Look again at the diagram of the standing wave on page 184 of the Student Book. For all standing waves, the whole spring goes through the equilibrium position twice in each wave cycle. As suggested above, the spring is moving at this time, so all of the energy in the spring is kinetic as the spring moves through the equilibrium position.
The most important wave properties are amplitude, frequency, wavelength, and speed. Frequency, wavelength, and speed are generally independent of amplitude. Consequently, when two waves pass through each other, the two amplitudes simply add at every point, as shown. This is the principle of superposition.
If you took a snapshot of the wave, with a meter stick right above the crests, you could measure the wavelength (the distance between adjacent crests). If you made a movie of the motion, with a clock in the frame, you could measure the frequency of the waves by timing one complete cycle. The period is simply the inverse of the frequency. Notice how the units invert as well. One hertz is a cycle per second. It is the inverse of the period, which is measured in seconds (cycles are dimensionless).
Suppose you are watching water waves washing over a rock. If you watch a particular crest for a time of one wave period, it moves one wavelength. The frequency gives the number of wave periods in one second. Thus the speed is simply the wavelength times the frequency.
A wave moves through a medium. The spring is the medium for Slinky® waves, water is the medium for water waves, and air is the medium for sound waves. But there is one wave that does not require a medium. That is the electromagnetic wave. Electromagnetic waves move freely through space, which is an excellent vacuum. The Sun gives off light and radio waves. Various distant objects in the universe give off every kind of electromagnetic radiation, and all these waves travel through the emptiness of space to reach the Earth.
In a standing wave, the spring vibrates but no waves are seen to move along its length. Standing waves occur only at certain frequencies, which correspond to simple patterns of motion. In the lowest-frequency standing wave on a spring, the spring bows out in the middle, with the ends, of course, fixed in place. If the frequency is doubled, there is a node, a point of no motion, in the middle of the spring. (See the drawings on page 185.)
In a standing wave, a small amount of oscillation with just the right frequency can excite a huge oscillation in the vibrating system, a phenomenon called resonance. Moving the frequency away from a resonant frequency produces disorganized motion with a very small amplitude.
Making Waves
Background Information
Waves are a collective phenomena. The neighboring parts of the wave medium—the matter the wave moves through—interact and propagate a disturbance from one place to another. For spring waves, each part of the spring influences the neighboring parts through the force of the stretched spring. A disturbance in one part of the spring creates forces on neighboring parts, and the disturbance moves. The disturbance is a stretching of the spring from its equilibrium position, which is a straight spring. In Activity 1, the students disturb this equilibrium by whipping one end of spring back and forth to make a pulse, as shown in the drawing on page 185 of the Student Book.
In the pulse, the spring coils are stretched. This stretching exerts forces on these coils and pulls them back toward the equilibrium position. The stretching also puts forces on the nearby parts of the spring. These forces are reaction forces. When part of the spring is pulled one way, these reaction forces pull adjacent parts the other way. That is how the pulse moves.
Notice that the spring does not have to be motionless to be in the equilibrium position. Look again at the diagram of the standing wave on page 184 of the Student Book. For all standing waves, the whole spring goes through the equilibrium position twice in each wave cycle. As suggested above, the spring is moving at this time, so all of the energy in the spring is kinetic as the spring moves through the equilibrium position.
The most important wave properties are amplitude, frequency, wavelength, and speed. Frequency, wavelength, and speed are generally independent of amplitude. Consequently, when two waves pass through each other, the two amplitudes simply add at every point, as shown. This is the principle of superposition.
If you took a snapshot of the wave, with a meter stick right above the crests, you could measure the wavelength (the distance between adjacent crests). If you made a movie of the motion, with a clock in the frame, you could measure the frequency of the waves by timing one complete cycle. The period is simply the inverse of the frequency. Notice how the units invert as well. One hertz is a cycle per second. It is the inverse of the period, which is measured in seconds (cycles are dimensionless).Suppose you are watching water waves washing over a rock. If you watch a particular crest for a time of one wave period, it moves one wavelength. The frequency gives the number of wave periods in one second. Thus the speed is simply the wavelength times the frequency.
A wave moves through a medium. The spring is the medium for Slinky® waves, water is the medium for water waves, and air is the medium for sound waves. But there is one wave that does not require a medium. That is the electromagnetic wave. Electromagnetic waves move freely through space, which is an excellent vacuum. The Sun gives off light and radio waves. Various distant objects in the universe give off every kind of electromagnetic radiation, and all these waves travel through the emptiness of space to reach the Earth.
In a standing wave, the spring vibrates but no waves are seen to move along its length. Standing waves occur only at certain frequencies, which correspond to simple patterns of motion. In the lowest-frequency standing wave on a spring, the spring bows out in the middle, with the ends, of course, fixed in place. If the frequency is doubled, there is a node, a point of no motion, in the middle of the spring. (See the drawings on page 185.)
In a standing wave, a small amount of oscillation with just the right frequency can excite a huge oscillation in the vibrating system, a phenomenon called resonance. Moving the frequency away from a resonant frequency produces disorganized motion with a very small amplitude.