Waves

1. Waves

2. Simple Harmonic Motion (SHM) Revisited • These motions may occur in a straight line but are closely related to circular motion • SHM - where acceleration is proportional to the displacement of the body from the center of the vibration and directed toward the center. • Examples: Mass on a spring, pendulum.

3. Characteristics of SHM • Amplitude – how far from equilibrium the object is displaced • Period - (T) – the time it takes for one vibration or oscillation to repeat itself (seconds) • Frequency - (ƒ) – the number of vibrations that occur in one second (s-1 or Hz) • ƒ = 1/T or T = 1/ƒ

5. Waves • When a wave passes under a boat, the boat moves. • To move it, work must be done. Work is energy  waves carry energy. • Particles and waves can carry energy. • Ex. Throwing a ball vs. shaking a rope.

6. Mechanical Waves • A disturbance in matter may cause a wave. • The matter becomes the medium through which the wave travels. • Mechanical waves must have a medium • A mechanical wave may propagate in a solid, liquid, or gas. • Ex. Water waves and sound waves. • Electromagnetic waves (coming soon) do not need a medium.

7. Pulses and Periodic Waves • Pulse - a single disturbance through a medium. • Ex. Crest of a wave • Periodic Wave - a series of evenly spaced (same frequency) disturbances or pulses. Can be called a wave train.

8. Transverse Waves (Type 1) • Disturbance is perpendicular to the direction of the wave motion.

9. Transverse Wave Parts • Crest - top of the wave • Trough - bottom of wave • Amplitude - height of the wave from the equilibrium position. (Determines amount of energy transmitted) • Wavelength() - distance from crest to crest, trough to trough, or corresponding point to corresponding point on adjacent pulses. (meters)

11. Longitudinal Waves (Type 2) • The disturbance is in the same direction as the direction of wave motion. • EX. Squeezing together several coils of a spring and releasing it. Sound waves.

12. Longitudinal Wave Parts • Compression - where the particles of the medium are close together. • Rarefaction(elongation) - particles are more spread out. • Wavelength - distance from compression to compression or rarefaction to rarefaction.

13. Amplitude of L - Waves • Greatest deviation in density or pressure from the norm. • Density graph. (Reuben’s Tube)

14. Finding The Speed of a Wave • Speed depends on the medium through which the wave travels. • Generally the denser the medium, the faster the wave travels. • v = d/t • = /T • = ƒ

15. Sample Problem #1 • A sound wave has a frequency of 262Hz and a wavelength measured at 1.29 m.

16. What is the period of the wave?

17. What is the speed of the wave?

18. How long will it take the wave to travel the length of a football field, 91.4m?

19. Sample Problem #2 • The speed of a radio wave is 3x108m/s. What is the wavelength of a radio wave whose frequency is 600kHz?

20. Wave Behavior at Boundaries • Incident wave - the initial pulse that strikes a boundary • Reflected wave - the returning wave from the boundary. • May be upright (erect) or downward (inverted) • May only be part of the energy contained in the incident wave • Transmitted wave - the wave that continues past the boundary. • May also only contain part of the energy in the incident wave.

21. Boundary of Two Media • The junction from a thicker media to a thinner media • Part of the incident wave is transmitted upright and part is reflected back upright. • The transmitted wave is always upright. • The reflected wave can be upright or inverted depending on the boundary. • If the second medium allows the wave to travel slower, the reflection will be inverted. EXAMPLE

22. A Rigid or Fixed Boundary • If the pulse hits a fixed boundary that does not move, most of the energy in the wave is reflected. • The wave cannot move that boundary so the boundary exerts a force in the opposite direction. • Reflected wave is inverted. • EXAMPLE

23. A Soft Boundary • The soft boundary is free to move with the wave and is theoretically frictionless. • The reflected wave is upright and because of the frictionless surface, no energy is lost to the boundary. • EXAMPLE

24. Wave Superposition • The displacement of the medium caused by two or more waves. • Total displacement is the sum of the two displacements. • If two waves traveling in opposite directions and have the same amplitude, meet in a medium, the point at which they meet will have an amplitude with a magnitude of twice the original amplitudes.

25. Interference • Constructive Interference - wave displacements are in the same direction. Results in a larger amplitude. • Destructive Interference - wave displacements are in opposite directions. Results in a smaller amplitude. • Demo

28. Standing Waves • These are examples of reflection and interference. • When the periodic wave is sent along a medium and reflects back on itself, at certain frequencies it will produce nodes and antinodes.

29. Nodes - points of destructive interference where the medium does not move. • Antinodes - points of construction where the medium moves at a maximum.

30. Wave Phase • Comparing the location of two waves in the same medium. • Points on one wave can also be in phase. • Two crests are in phase. • A crest and a trough are 1800 out of phase. • If two waves are 1800 out of phase, they will destructively interfere. • If they are in phase, they will constructively interfere.

31. Wave Reflection • When an incident wave approaches a barrier it will reflect off of the barrier and an angle equal to the incidental angle. • i = r

32. Diffraction • When a wave passes through a hole in a barrier, it will form a circular wave pattern as it radiates outward. • The edge of the barrier slows that portion of the wave creating the circular pattern.

33. Having two holes in the barrier creates two circular waves that will interfere with each other. • There will be nodal lines(destructive interference) and antinodal lines(constructive interference).