Chapter 13

1. Chapter 13 Mechanical Waves

2. Propagation of A Disturbance • What are waves? • Waves are traveling disturbances or vibrations. • Waves carry energy from place to place • There are 2 types of waves: • Transverse (example: light, electromagnetic waves) • Disturbance is perpendicular to direction of wave propagation • Longitudinal (example: sound waves) • Disturbance is parallel to direction of wave propagation

3. Propagation of A Disturbance • What are waves? • Waves are traveling disturbances or vibrations. • Waves carry energy from place to place • There are 2 types of waves: • Mechanical waves • Disturb and propagate through a medium • Electromagnetic waves • Do not require a medium in order to propagate.

4. All mechanical waves require • Some source of disturbance; • A medium; • Some physical mechanism through which particles of the medium can influence one another. stretched compressed source P

5. vt v The Wave Function (a) Pulse at t=0 A P P P P O vt (b) Pulse at time t P at x at time t has the same y positon as an element located at x-vt at time t=0 P y(x,t) = y (x-vt,0) Represent y for all positions and times, measured at O: O y(x,t) = f (x-vt), f(x) is the shape of the pulse

6. The Wave Function • Wave travels to the right y(x,t) = f (x-vt) • Wave travels to the left y(x,t) = f (x+vt) • The function y called the wave function, depends on the two variables x and t. • The wave function y(x,t) represents the y coordinate of any point P located at position x at any time t.

7. The Wave Model y l l • One wavelength is the minimum distance between any two identical points on a wave. • The period T of the wave is the minimum time it takes a particle of the medium to undergo one complete oscillation. • T = 1 / f • The amplitude A is the maximum displacement of a particle of the medium from the equilibrium position. • The wave speed v is the distance travelled by the wave in one second. A A x y T A t

8. Properties of Periodic Waves • All waves share 3 properties: • The propagation speed of the wave, v • The spacial length of a wave from crest to crest is called its wavelength, l • The rate (or frequency) of vibration describes how fast a wave oscillates, f • The propagation of a wave is related to its wavelength & its frequency: v = l/T = l.f • The speed of wave depends on the properties of the material (medium) where the wave travels. • For a wave on a string: • Where: • F = tension in the string • m = mass of the string • L = length of the string

9. The Traveling Wave y Blue t=0 Red t • A sinusoidal wave x

10. The Traveling Wave Assumed y=0 at x=0 and t=0 If y≠0 at x=0 and t=0

11. The Traveling Wave y(cm) A=15.0cm; A wavelength 40.0cm; A frequency 8.00Hz; The vertical displacement of the medium at t=0 and x=0 is also 15.0cm. 40.0cm 15.0cm x(cm)

12. The Traveling Wave y(cm) A=15.0cm; A wavelength 40.0cm; A frequency 8.00Hz; The vertical displacement of the medium at t=0 and x=0 is also 15.0cm. 40.0cm 15.0cm x(cm)

13. Reflection & Transmission of Waves • If the end is fixed then the pulse is reflected and undergoes a phase change of 180 degrees or half a period, so a crest become a trough and vice versa. • Reflected pulse is inversed. Lower density

14. Reflection & Transmission of Waves • If the end is free to move then reflection but no inversion takes place. Higher density

15. Reflection & Transmission of Waves • Inversion will always be observed when the end of the medium is fixed. When two media are connected and the pulse travelling through a medium meets a denser medium it is partially reflected and partially transmitted. The reflected part is inverted as for the fixed end. • If instead the pulse meets a lighter medium it is partially reflected and partially transmitted but undergoes no inversion.

16. Applications • Ultrasound image

17. Sound Waves • Longitudinal wave • Produced by vibrations in a medium • The disturbance is the local change in pressure generated by the vibrating object • It travels because of the molecular interactions. • The region of increased pressure( compared to the undisturbed pressure) is called condensation • The region of lower pressure is called rarefaction. • The maximum increase in pressure is the amplitude of the pressure wave. (measurable) • Frequency of the sound 20Hz to-20000Hz. • Pressure waves below 20 Hz are called infrasonic waves • Pressure waves over 20,000Hz are called ultrasonic waves.

18. The Speed of Sound • Speed of sound depends on the compressive properties of the medium. • Because of the high frequencies, the compression/expansions are fast and no heat is exchanged (adiabatic). • Sound can travel in gases, liquids and solids. • The speed of sound in gases: • The speed of sound in liquids: • The speed of sound in solids:

19. The Speed of Sound • The speed of sound in gases depends on temperature. In 20 °C (68 °F) air at the sea level, the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph) using the formula "v = (331 + 0.6 T) m/s". • In fresh water, also at 20 °C, the speed of sound is approximately 1,482 m/s (5,335 km/h; 3,315 mph). • In steel, the speed of sound is about 5,960 m/s (21,460 km/h; 13,330 mph).

20. 发射频率 接收频率 The Doppler Effect • The frequency of the source producing the wave equals the number of cycles per second. • The frequency measured by an observer is the number of crests (condensations) encountered per second. • When both the source and the observer are at rest, the 2 frequencies are equal. • When one or both are in motion, the 2 frequencies are different. • The difference between source and observed frequency is called Doppler shift.

21. The Doppler Effect • Moving source, observer at rest • The wavelength is changed because of the relative motion of source and observer Source moving toward observer Source moving away from the observer Notes: vs = speed of source v = speed of sound fs = frequency of source

22. The Doppler Effect • Moving observer, source at rest • The time between encountering 2 crests changes for observer Observer moving toward source Observer moving away from source Notes: vo = speed of observer v = speed of sound fs = frequency of source

23. The Doppler Effect

24. The Doppler Effect • Red shift. • The big bang theory.

25. The Seismic Waves • P wave: longitudinal wave, higher speed • S wave: transverse wave, lower speed

26. The Seismic Waves • Only P waves (yellow) can propagate in the liquid core.

27. The Seismic Waves

28. The Seismic Waves • P wave: longitudinal wave, higher speed vp=9.1km/s • S wave: transverse wave, lower speed vs=3.7km/s • If the epicenter is l=20km bellow the surface, you will have Dt=l/vp-l/vs =20/3.7 – 20/9.1 =3.21 second to escape!

29. Earthquake Safety Rules During the earthquake: • Do not panic, keep calm. • Douse all fires. • If the earthquake catches you indoors, stay indoors. Take cover under a sturdy piece of furniture. Stay away from glass, or loose hanging objects. • If you are outside, move away from buildings, steep slopes and utility wires. • If you are in a crowded place, do not rush for cover or to doorways. • If you are in a moving vehicle, stop as quickly as safety permits, but stay in the vehicle until the shaking stops. • If you are in a lift, get out of the lift as quickly as possible. • If you are in a tunnel, move out of the tunnel to the open as quickly as safety permits.

30. Earthquake Safety Rules After the earthquake: • Check for casualties and seek assistance if needed. • If you suspect a gas leak, open windows and shut off the main valve. Leave the building and report the gas leaks. Do not light a fire or use the telephone at the site. • Turn off the main valve if water supply is damaged. • Do not use the telephone except to report an emergency or to obtain assistance. • Stay out of severely damaged buildings as aftershocks may cause them to collapse. Report any building damage to the authorities. • As a precaution against tsunamis, stay away from shores, beaches and low-lying coastal areas. If you are there, move inland or to higher grounds. The upper floors of high, multi-storey, reinforced concrete building can provide safe refuge if there is no time to quickly move inland or to higher grounds.