What should I know?

1. Objects or particles that are held in place by a set of forces can be made to oscillate around their rest position due to the action of those restoring forces.

2. These restoring forces can sometimes be modeled with springs.

3. When springs are stretched, they pull inward with a force that is proportional to the amount that they are stretched.

4. When springs are compressed, they push outward with a force that is proportional to the amount they are compressed.

5. Hooke’s law states that the force applied by a spring is in a direction opposite of the direction of the change of the length of the spring. It also states that the amount of the force the spring applies when the spring’s length is changed is determined by the stiffness of the spring.

6. Like the forces applied by springs, restoring forces have a positive correlation with the amount of displacement of the object or particle.

7. Objects or particles can be displaced from their rest positions by doing work on them, which gives them potential energy. This energy is converted into kinetic energy by the restoring forces.

8. Objects or particles that are displaced from their rest positions will continue to move past their rest positions due to their inertia and the fact that the net force acting on the object or particle decreases to zero at the rest position.

9. Objects that show a repetitive vibration around a central point due to restoring forces that are proportional to the displacements of the objects are in simple harmonic oscillation or simple harmonic motion (SHM).

10. At the object’s rest position -- the point at which it experiences no net force -- its kinetic energy is a maximum and its potential energy is zero.

11. One critical measurement of the nature of a particular instance of SHM is its period, which is a measure of the time required for the object to move through one complete oscillation. Period is measured in seconds.

12. The period of oscillation is the inverse of the frequency of its oscillation. Frequency is measured in hertz.

13. Two examples of SHM are simple pendula and spring pendula.

14. For spring pendula: a bob oscillates around a rest position with a spring providing all or part of the restoring force.

15. For simple pendula: a bob swings back and forth on a string, with the combination of gravity and the tension on the string providing the restoring force.

16. If work is done on particles in a matrix, the energy added to the particles is transmitted to the neighboring particles through the restoring forces; this transmission of energy takes the form of a wave. 

17. Waves come in two main types, based on a comparison of the directions of the vibration and the wave's propagation: in longitudinal waves, particles oscillate parallel to the direction of the wave's propagation; in transverse waves, the particles oscillate perpendicular to the wave's propagation.

18. Waves transmit energy through a medium, not matter.

19. Transverse waves have certain characteristics:

    • crest - the wave’s highest point

    • trough - wave’s lowest point

    • amplitude - the maximum distance the medium moves away from its rest position.

    • wavelength - the distance between two successive crests or two successive troughs

20. Longitudinal waves have certain characteristics:

    • compression - a point of highest pressure or density

    • rarefaction - a point of lowest pressure or density

    • amplitude - the maximum distance the medium moves away from its rest position.

    • wavelength - the distance between two successive crests or two successive troughs

21. Waves move at a speed that is dictated by the nature of the medium. No other wave property can affect the wave's speed.

22. Wave speed and frequency are related but often confused for each other.

23. A phenomenon is a wave if it exhibits the four wave behaviors: 

    • reflection - a bouncing off a rigid boundary, 

    • refraction - a bending as it moves from one type of medium to another, 

    • diffraction - a bending around barriers, and 

    • interference - interaction between two or more waves, which affects the total amplitude of particles in the medium at that point.

24. For a source moving through a medium, producing waves as it goes, the speed of the waves produced is not affected but the frequency of those wave changes based on the direction of motion of the source. This phenomenon is known as the Doppler effect.

25. For a source moving at a speed that is the same or greater than the waves it produces, the waves produced constructively interfere, creating a shock wave. 

26. Sound is a type of longitudinal wave, which may be transmitted through many types of media, but is most commonly described as transmitted through air.

27. Waves in a closed tube or on a string with fixed ends can produce standing waves if oscillated at certain frequencies. Those frequencies are determined by the length of the tube or the string and the speed at which the waves propagate. Standing waves are also called harmonics due to the fact that they are closely associated with the notes produced by musical instruments.

28. Humans experience sound wave properties in different ways: the amplitude is related to the loudness of the sound experienced and the frequency of the sound wave is interpreted as the sound's pitch.

29. The range of hearing of a healthy young human is 20 to 20,000 Hz.

30. The range of loudness that can be experienced safely by a human is 0 to 120 decibels; above this range, permanent hearing loss will occur.

31. The musical nature of certain sounds results from the patterns produced; the human brain can decipher these patterns and appreciate their beauty. 

32. Musical instruments produce the musical notes that they produce due to the length of their open- or closed-end tubes or strings.