1. Damping Sometimes engineers don’t want springs to keep oscillating.
They employ damping to remove the oscillatory energy from the spring.
Shock absorbers in cars are a good example: they are designed to damp out oscillations and produce a smooth ride.

2. Natural frequency
The frequency at which a system tends to oscillate is called its natural frequency.
Each string on a guitar oscillates with a different natural frequency.
A guitar string that plays the note middle C has been tuned to have a natural frequency of 262 Hz.

3. Resonance
Resonance occurs when the periodic force is applied at the natural frequency.

4. Transverse waves
A transverse wave causes oscillations that are perpendicular to the forward motion of the wave.
Examples:
waves in a string
light waves

5. Longitudinal waves
A longitudinal wave causes oscillations that move back and forth in the same direction as the traveling wave.
Examples:
sound waves
the waves in a spring as shown in this figure
Move a Slinky® rapidly forward and back to create a longitudinal compression wave.

6. Describing waves- more terms
A crest represents all the high points in a wave.
A trough is all the low points in the wave.

7. Boundaries
Reflection occurs at boundaries where conditions change—such as the edge of a pool or a wall in a room.
The kind of reflection that occurs depends on whether the boundary is fixed or open.

8. Fixed boundaries A fixed boundary does NOT move in response to a wave.
The wave pulse reflects on the opposite side of the spring.
This behavior can be explained with Newton’s third law. The incoming pulse in the spring pulls UP on the wall, and the wall pulls DOWN on the spring.

9. Open boundaries
An open boundary allows the end of the spring to move freely.
The wave reflects on the same side of the spring as the incident wave.

10. Refraction
Refraction occurs when a wave changes speed at a boundary, resulting in a change of direction.
Water waves refract if the depth changes.
They refract because they move slower in shallow water than in deep water.

11. Refraction and frequency
Recall:
When wave velocity changes during refraction, the wavelength also changes.
But frequency CAN’T change:
Every wave that enters the boundary must exit the boundary. Therefore, the number of waves per second must stay constant.

12. Diffraction
Diffraction is a property of waves that allows them to bend around obstacles and pass through gaps.
Diffraction often changes the direction and shape of a wave.

13. Superposition principle
The superposition principle says that the total amplitude at any point equals the sum of the amplitudes of all of the waves that occur at that same place and time.

14. Constructive interference
When more than one wave is present, they can combine to make a larger or smaller amplitude wave.
If the result is a larger amplitude wave, constructive interference has occurred.

15. Destructive interference
Two waves can also add up to
make a smaller wave.
When two or more waves add
up to make a smaller amplitude wave, destructive interference has occurred.
If the amplitudes are exactly matched, there can be total destructive interference.

16. Standing waves
Standing waves occur when a wave and its reflection interfere constructively. To make a standing wave, continuously launch wave pulses by shaking one end of a spring.
If the rhythm is just right, each new pulse adds constructively to the reflection of the previous pulse.

17. Nodes and antinodes
A node is a stationary point where the amplitude stays zero.
An antinode is a point of maximum amplitude.

18. Natural frequencies At different frequencies, different standing wave
patterns appear on a vibrating string.
The fundamental is also called the first harmonic.
The lowest frequency and longest wavelength wave is the fundamental.

19. Natural frequencies At different frequencies, different standing wave
patterns appear on a vibrating string.
The lowest frequency and longest wavelength wave is the fundamental.
The next higher frequency wave is the second harmonic,
at twice the frequency of the fundamental.

20. Natural frequencies
The third harmonic has three times the frequency of the fundamental, and so on.
Each harmonic is a vibrating mode of the string.
A mode is a characteristic pattern of vibration that occurs at a resonant frequency of the system.
The natural frequencies of a system are the frequencies of its resonant modes.

21. Applications of resonance
Technologies such as musical instruments and microwave ovens are systems designed to create resonance at the desired frequencies.