IB Physics Oscillations and Waves

1. IB PhysicsOscillations and Waves

2. The 5 Properties of Waves • Rectilinear Propagation: waves propagate (move or spread out) in straight lines in all directions away from the source. ( s = v∙t ) • Reflection: change in direction of a wave at an interface between two different media so that the wave returns into the medium from which it originated. ( m ∠i = m∠r ) • Refraction: change in direction of a wave due to a change in its speed. Observed when a wave passes from one medium to another. (Snell’s law.)

3. Reflection (from a fixed end) (Boundary behavior.)

4. Reflection (from a loose end) (Boundary behavior.)

5. The 5 Properties of Waves (con’t.) • Diffraction: bending of waves around small obstacles and the spreading out of waves passing through small openings. • Interference: the addition (superposition) of two or more waves that results in a new wave pattern.

6. 2) Longitudinal – the disturbance is parallel to the direction the wave is traveling Any Wave: is a traveling disturbance that carries energy. Two types of waves: 1)Transverse – the disturbance is perpendicular to the direction the wave is traveling

7. y  A A x Consider a transverse wave on a string, frozen in time:  = wavelength A = Amplitude • From research, we have: • The wave equation: v = f  • Velocity = Frequency x wavelength • 2. Period (T): time in seconds for a wave to pass by. • 3. Frequency (f): number of waves per second, or Hertz, Hz. T = period f = frequency T = 1/f

8. If the wave crests are 12 m apart, and you see one pass by you every 3 seconds, how fast are they going? v = f  Frequency (f), period (T), wavelength (), and wave speed (v) are all related: v = /T f = 1/T

9. Ex: Radio Waves 2.81 m How long do you think the wavelengths of radio waves are ? Radio waves are a type of Electromagnetic Wave Radio waves travel at the speed of light in a vacuum, 3.00 x 108 m/s . Find the wavelength of radio waves from station 106.7 M Hz.

10. Electromagnetic Waves These don’t need a medium (substance to travel in).

11. v = f  That means that these two are inversely proportional f f All other waves require a medium (air, water, string, etc.) The speed of a wave depends on the medium.

12. v Waves on a String Researchers have developed a formula for the speed of waves on a string: What qualities of the string do you think determine this speed? Tension, mass, length? All 3. v = √(F/µ) , µ=m/L

13. Ex: The rope has a length of 1.2 m and a mass of 2.0 kg. If he shakes the end 4.0 times a second, and it yields the pattern shown, what is the tension in the rope?

14. Sound waves in air consist of vibrating air molecules Sound Waves *any longitudinal waves

15. Compare a longitudinal wave in a slinky to a sound wave in a tube:

16. very small for common sounds ( 3x10-2 Pa) • A = pressure amplitude = max. change in pressure • Loudness is related to pressure amplitude

17. Healthy young ears can hear frequencies between: 20 Hz 20,000 Hz Infrasonic Which end do we lose with age? Ultrasonic Frequency of Sound Waves: number of cycles per second • Pure tone – a single frequency sound (most sounds are composed of many frequencies)

18. Ex: Lightning & Thunder Speed of Sound depends on the medium (gas, liquid or solid) vsound in air = 343 m/s (767 mi/hr) Mach 1 Lightning and thunder occur at the same time.

19. Speed of sound in an ideal gas k = 1.38 x 10-23 J/K (Boltzmann const.) T = Kelvin temperature m = molecular mass in kg  = CP/CV (the Adiabatic constant) For air (mostly O₂ and N₂),  = 1.40

20. Ex: Verify the speed of sound in 20.0⁰C air if the average air molecule mass is 28.9 u, and = 1.40 for air.

21. Bulk Modulus (adiabatic) Density of the liquid. Water? Ex: Water, Speed of sound in a liquid Bad ≈2.25 G Pa9 , increases with pressure The speed of sound in water is around _____ m/s (that’s over __ times as fast as it travels in air!)

22. Young’s Modulus, divided by density Ex: Train Tracks, steel, Y ≈ 200 G Pa, ρ ≈ 7700 kg/m3 Speed of sound in solid bars Find: Speed of sound in steel.

23. Sound Intensity = of the sound wave  to the wave Sound Intensity SI unit = W/m2

24. Area = 4r2 Ex: Fireworks 600 m 200 m Spherically Uniform Sound: How much less is the sound intensity for the person that is farther away?

25. Intensity is related to loudness (but not directly proportional) To compare two intensities (I and I0):  (in decibels) = 10 log (I/I0) “Intensity Level” (unitless) For sound meters, I0= threshold = 10-12 W/m2 Notes on Sound Intensity • 10-12 W/m2 = lower threshold of human hearing • 1 W/m2 = enough to cause ear damage • Different sound intensities are comparedusing:decibels (dB)

26. Ex: If a sound meter picks up an intensity of 1.0 x 10-5 W/m2 , what will be the intensity level reading in dB?

28. The Doppler Effect- the change in wave frequency resulting from motion of the source or observer Consider the waves from a sound source: Now, consider the waves from a moving source: You hear a lower frequency as it moves away from you You hear a higher frequency as it moves toward you

29. Source moves toward still observer Source moves away from still observer Here’s how to calculate the frequency heard by the observer: f’ = perceived frequency vs = speed of the source f = actual frequency v = speed of the wave

30. Ex: If the fire engine has a speed of 30 m/s, and its siren has a frequency of 500 Hz, what frequency does the pedestrian hear as it moves • toward him ? • away from him ?

31. toward the source: away from the source: Now, if the observer is moving at speed vO…..

32. vs vo (signs determined as before) Now, if both observer and source are moving…

33. wavelength size of obstacle tiny for light larger for sound (better dispersion) All waves exhibit diffraction, including sound. • The extent of diffraction is determined by this ratio:

34.  D  D Diffraction of Sound Waves For a single slit (or doorway) of width D : Angle of 1st diffraction minimum For a circular opening of diameter D : Angle of 1st diffraction minimum

35. Beat Frequency Refers to the rate at which the volume is heard to be oscillating from high to low volume. The beat frequency is always equal to the difference in frequency of the two notes that interfere to produce the beats. So, with frequencies of 256 Hz and 254 Hz, a beat frequency of 2 Hz will be detected. fbeat = f1 – f2

36. Standing Waves in Open and Closed Tubes: (Based on Resonance) closed:/4, 3/4, 5/4, … odd. mult. open: /2, , 3/2, 2, … all mult.

37. The intensity I of the light transmitted by the analyzer is directly proportional to the square of the cosine of the angle between the transmission axes of the analyzer and the polarizer. Étienne-Louis Malus (1775-1812)

38. n Brewster’s Angle: Named after the Scottish physicist Sir David Brewster (1781–1868). When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. (n = index of refraction) n = tan(θ)

39. toward away OSCILLATIONS AND WAVES: Equations and constants. s = v∙t m ∠i = m∠r v = f  f = 1/T Ve/m waves,v = 3.00 x 108 m/s vwave in string, v = √(F/µ) µ=m/L vsound in ideal gas, k = 1.38 x 10-23 J/K m = molecular mass, 1.67 x 10-27 kg  = cP/cV (Adiabatic constant) For air (mostly O₂ and N₂),  = 1.40 vsound in air = 331.5 m/s @ 0.0 °C, + .6 (m/s)/°C vsound in liquid, vsound in solid, I = P/4πr2  (in decibels) = 10 log (I/I0) I0= 1.0x10-12 W/m2 fbeat = f1 – f2 n = tan(θ) I = I0cos2(θ) closed:/4, 3/4, 5/4, … odd. mult. open: /2, , 3/2, 2, … all mult.