Vibrations and Waves

1. Vibrations and Waves Chapter 25

2. Vibration of a Pendulum • Vibration – a wiggle in time • A vibration cannot exist in one instant, but needs time to move back and forth • Wave – a wiggle in space and time • A wave cannot exist in one place, but must extend from one place to another • Period – the time of a back-and-forth swing of a pendulum, depends only on the length of the pendulum and the acceleration of gravity (T = 2π√(L/g)) • A long pendulum has a longer period than a shorter pendulum

3. Wave Description • Simple Harmonic Motion – the back-and-forth vibratory motion of a swinging pendulum • When a pendulum is placed over a moving conveyor belt, which allows a trace of the motion, the pendulum will trace out a sine curve • A sine curve is a pictorial representation of a wave

4. Simple Harmonic Motion

5. Wave Description • Crest – high point on a wave • Trough – low point on a wave • Amplitude – the distance from the midpoint to the crest • The amplitude equals the maximum displacement from equilibrium • Wavelength – the distance from the top of one crest to the top of the next one (or between successive identical parts of the wave) • Frequency – describes how often a vibration occurs, units are in Hertz (Hz = 1 cycle/second) Frequency = 1/Period (Hz) Period = 1/Frequency (s)

6. Wave Description

7. Wave Motion • When energy is transferred by a wave from a vibrating source to a distant receiver, there is no transfer of matter between the two points • The energy transferred from a vibrating source to a receiver is carried by a disturbance in a medium, not by matter moving from one place to another within the medium

8. Wave Motion

9. Wave Speed • The speed of a wave depends on the medium through which it travels • Whatever the medium, the speed, wavelength, and frequency of the wave are related Wave speed = wavelength X frequency (measured in m/s) v = λf • Sound waves move at speeds of about 330 m/s to 350 m/s in air, and four times faster in water

10. Wave Speed Problem The water waves below are traveling with a speed of 2 m/s and splashing periodically against the Wilbert's perch. Each adjacent crest is 4 meters apart and splashes Wilbert’s feet upon reaching his perch. How much time passes between each successive drenching?

11. Transverse Waves • Transverse Waves – the motion of the medium is at right angles to the direction in which the wave travels • Examples: stretched strings in musical instruments, waves on surfaces of liquids, radio waves, light waves, and s-waves (earthquakes)

12. Transverse Waves

13. Longitudinal Waves • Longitudinal Waves – particles move along the direction of the wave rather than at right angles to it • Examples: sound waves and p-waves (earthquakes)

14. Longitudinal Waves

15. Interference • Interference Pattern – within a pattern, wave effects may be increased, decreased, or neutralized • Constructive Interference (reinforcement) – the crest of one wave overlaps the crest of another, their individual effects add together producing an increased amplitude • Destructive Interference (cancellation) – the crest of one wave overlaps the trough of another, their individual effects are reduced • When waves produce areas of zero amplitude, they are “out of phase” • When the crest of one wave overlaps the crest of another, they are “in phase”

16. Interference

17. Standing Waves • Standing Wave – certain parts of the wave remain stationary, when the incident wave and reflected wave meet • Nodes – part of the standing wave which does not move and has no amplitude (at equilibrium) • Antinodes – position on a standing wave which has the largest amplitude • When two waves of equal amplitude and wavelength pass through each other in opposite directions, they are always out of phase at the nodes and in phase at the antinodes

18. Formation of Standing Waves

19. The Doppler Effect • Doppler Effect – the apparent change in frequency due to the motion of the source (or receiver) • Spherical sound or light wave crests ahead of a moving source are closer together than those behind the source and encounter a receiver more frequently • Blue Shift – an increase in frequency towards the high-frequency, or blue, end of the light spectrum (light source is moving towards receiver) • Red Shift - a decrease in frequency towards the low-frequency, or red, end of the light spectrum (light source is moving away from the receiver) • Distant galaxies show a red shift in the light they emit, indicating that the universe is expanding (or moving further apart)

20. The Doppler Effect

21. Blue Shift and Red Shift

22. Bow and Shock Waves • Bow Wave – when the speed of the source in a medium is as great, or greater, than the speed of the wave it produces it will catch up to the wave crests and pass them producing a v-shape • Shock Wave – like a bow wave, but in three dimensions, produces a cone-shape • Sonic Boom – produced when the conical shell of compressed air that sweeps behind a supersonic jet reaches listeners on the ground below

23. Bow and Shock Waves

24. Assignment • Read Chapter 25 (pg. 372-386) • Do Chapter 25 Assessment #21-41 (pg. 388-389)