Sound waves

Transcription

1 Types of waves

2 Sound waves

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5 Violin A 440Hz

6 Guitar A 440Hz

7 Piano A 220Hz

8 Recorder A 880Hz

9 Flute A 440Hz

10 Rubens tube

11 Earthquakes

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19 Mavericks, California

20 Garrett McNamara surfs a 100ft wave! (January 2013, off the coast of Portugal)

21 Garrett McNamara surfs a 100ft wave! watch?v=5xpu5m0zckm

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23 Ripples and caustics Surface tension is important!

24 A wake is an interference pattern of waves formed by the motion of a body through a fluid. Intriguingly, the angular width of the wake produced by ships (and ducks!) in deep water is the same (about 38.9 o ). A mathematical explanation for this phenomenon was first proposed by Lord Kelvin ( ). The triangular envelope of the wake pattern has since been known as the Kelvin wedge. 24

25 The Kelvin Wedge 2sin o Note tan sin

26 In general, for vorticity free waves on the interface of two incompressible, Newtonian fluids, the dispersion relationship can be shown to be, for waves with amplitude G<< D surface tension 2 3 k g 1 2 k 1cotanh 2 kd For waves on a water, air interface 2 k 1 3 gk tanh kd fluid densities , so ignore 2 For shallow water waves tanhkd kd 2 4 k D 2 gk D 1 depth For deep water waves tanhkd k gk 1 26

27 Since k 2 the higher powers of k will contribute less for longer wavelengths Hence for shallow water gravity waves e.g. waves coming ashore just before they break, or waves in a shallow river or canal 2 gk 2 D cp k gd Similarly for deep water waves 2 gk c p g k k g 2 Note for deep water ripples (or capillary waves ) this approximation is invalid. We must use the full dispersion relation Ripple phase velocity is: 3 k gk 1 Water: = 1000 kgm -3 = Nm -1 c p k g 2 g k k Which has a minima at c p 4 4 g 1 minimum phase velocity = 23 cms -1 27

28 Lenticular clouds

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30 Kelvin Helmholtz instability on Earth

31 Kelvin Helmholtz instability on Jupiter

32 Shock waves

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34 Convert wavelength into frequency using c f c ms 8 1

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36 NASA space telescopes Compton Hubble Spitzer

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39 Note solar energy is absorbed in atmosphere by oxygen, water vapour, carbon dioxide etc. Hence dips in the solar spectra at sea level. Measure surface temperature of a star from the spectral shape This theoretical curve is called the Black-Body spectrum (i.e. brightness at different wavelengths) Convert wavelength into frequency using c f

40 Hertzsprung- Russell diagram 1910 by Ejnar Hertzsprung and Henry Norris Russell

41 Doppler shift method for measuring radial velocity c f If an object emitting radiation at frequency f moves radially towards an observer at velocity v, the observer will measure a slightly higher frequency of radiation as the emitted waves bunch up. frequency change Velocity of emitter towards observer f v c f Frequency of emitted radiation Speed of radiation v Note this formula is Classical. It is valid when v << c, otherwise a relativistic version must be used Christian Doppler

42 Redshift z is the fractional change in wavelength of light due to the Doppler effect z observed emmitted emmitted

43 Convert wavelength into frequency using c f c ms 8 1

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45 Convert wavelength into frequency using c f c ms 8 1

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47 GSM spectrum (microwaves) 380 MHz 1.8GHz Global System for Mobile Comminication (GSM) first deployed in Finland in July 1991

48 Convert wavelength into frequency using c f c ms 8 1

49 Infra Red

50 Convert wavelength into frequency using c f c ms 8 1

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52 Convert wavelength into frequency using c f c ms 8 1

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54 Convert wavelength into frequency using c f c ms 8 1

55 X-Rays

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57 Convert wavelength into frequency using c f c ms 8 1

58 Gamma Rays

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60 Convert wavelength into frequency using c f c ms 8 1

61 Gravitational waves emitted from two colliding black holes (!)

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63 Pulsars were discovered by accident in 1967 while Jocelyn Bell and Antony Hewish were looking for twinkling sources of radio radiation. The explanation for the radio pulses proved the existence of neutron stars, incredibly dense remains of massive collapsed stars.

64 Pulsars

65 The 76 m Lovell Telescope at Jodrell Bank Observatory (Cheshire)

66 Multi-Element Radio Linked Interferometer Network (MERLIN)