Waves and Sound

1. Waves and Sound October 26, 2012

2. Mechanical Wave • A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium.

3. crest equilibrium trough Parts of a Wave y(m) : wavelength 3 A: amplitude x(m) 2 4 6 -3

4. Speed of a wave • The speedof a wave is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. • v = d/t • d: distance (m) • t: time (s) • v = ƒ • v : speed (m /s) •  : wavelength (m) • ƒ : frequency (s–1, Hz)

5. Period of a wave • Period of a wave is the time it takes for one complete wave • T = 1/ƒ • T : period (s) • ƒ : frequency (s-1, Hz)

6. Problem: Sound travels at approximately 340 m/s. How far away is a lightning strike if the sound of the thunder arrives at a location 2.0 seconds after the lightning is seen?

7. Physics Challenge A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. The speed at which waves propagate on the string is • 0.4 m/s • 2.5 m/s • 5 m/s • 10 m/s • 20 m/s

8. Problem: The frequency of an oboe’s A is 440 Hz. What is the period of this note? What is the wavelength? Assume a speed of sound in air of 340 m/s.

9. Types of WavesRefraction and Reflection October 26, 2012

10. Wave Types A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. Example: Waves on a String A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. These are also called compression waves. Example: sound

11. Slinky Wave Demo

12. Other Wave Types • Earthquakes: combination • Ocean waves: surface • Light: electromagnetic

13. Physics Challenge An object is attached to a spring and oscillates with amplitude A and period T, as represented on the graph above. The nature of the velocity v and acceleration a of the object at time T/4 is best represented by which of the following? (A) v > 0, a > 0 (B) v > 0, a < 0 (C) v > 0, a = 0 (D) v = 0, a < 0 (E) v = 0, a = 0

14. Reflection of waves • Occurs when a wave strikes a medium boundary and “bounces back” into original medium. • Completely reflected waves have the same energy and speed as original wave.

15. Reflection Types • Fixed-end reflection: The wave reflects with inverted phase. • Open-end reflection: The wave reflects with the same phase

16. Refraction of waves • Transmission of wave from one medium to another. • Refracted waves may change speed and wavelength. • Refraction is almost always accompanied by some reflection. • Refracted waves do not change frequency.

17. Sound is a longitudinal wave • Sound travels through the air at approximately 340 m/s. • It travels through other media as well, often much faster than that! • Sound waves are started by vibration of some other material, which starts the air moving.

18. Physics Challenge One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown above. and is reflected at the wall. Properties of the reflected pulse include which of the following? I. It has a greater speed than that of the incident pulse. II. It has a greater amplitude than that of the incident pulse. III. It is on the opposite side of the string from the incident pulse. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

19. Physics Challenge A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning fork makes one complete vibration, the emitted wave travels • one wavelength • about 340 meters • a distance directly proportional to the frequency of the vibration • a distance directly proportional to the square root of the air density • a distance inversely proportional to the square root of the pressure

20. Pure Sounds • Sounds are longitudinal waves, but if we graph them right, we can make them look like transverse waves. • When we graph the air motion involved in a pure sound tone versus position, we get what looks like a sine or cosine function. • A tuning fork produces a relatively pure tone. So does a human whistle. • Later in the period, we will sample various pure sounds and see what they “look” like.

21. Graphing a Sound Wave

22. Hearing Sounds • We hear a sound as “high” or “low” depending on its frequency or wavelength. Sounds with short wavelengths and high frequencies sound high-pitched to our ears, and sounds with long wavelengths and low frequencies sound low-pitched. The range of human hearing is from about 20 Hz to about 20,000 Hz. • The amplitude of a sound’s vibration is interpreted as its loudness. We measure the loudness (also called sound intensity) on the decibel scale, which is logarithmic.

23. Doppler Effect • The Doppler Effect is the raising or lowering of the perceived pitch of a sound based on the relative motion of observer and source of the sound. • When a car blowing its horn races toward you, the sound of its horn appears higher in pitch, since the wavelength has been effectively shortened by the motion of the car relative to you. • The opposite happens when the car races away.

24. Doppler Effect Stationary source Moving source Supersonic source

25. Physics Challenge • A small vibrating object S moves across the surface of a ripple tank producing the wave fronts shown above. The wave fronts move with speed v. The object is traveling in what direction and with what speed relative to the speed of the wave fronts produced? DirectionSpeed (A) To the right Equal to v (B) To the right Less than v (C) To the right Greater than v (D) To the left Less than v (E) To the left Greater than v

26. Physics Challenge A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown above, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest? (A) A (B) B (C) C (D) D (E) It will be the same at all four points.

27. Superposition of Waves November 24, 2008

28. Principle of Superposition • When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the sum of the displacements due to each individual wave. • The wavesinterfere with each other.

29. Types of interference. • If the waves are “in phase”, that is crests and troughs are aligned, the amplitude is increased. This is called constructive interference. • If the waves are “out of phase”, that is crests and troughs are completely misaligned, the amplitude is decreased and can even be zero. This is called destructive interference.

30. crests aligned with crest Constructive Interference waves are “in phase”

31. Constructive Interference

32. crests aligned with troughs Destructive Interference waves are “out of phase”

33. Physics Challenge • Two wave pulses are traveling toward each other along a rope as shown above. When both pulses are in the region between points X and Y, which are a distance λ. Apart, the shape of the rope will be which of the following?

34. Destructive Interference

35. Physics Challenge The figure above shows two wave pulses that are approaching each other. Which of the following best shows the shape of the resultant pulse when the centers of the pulses, points P and Q, coincide?

36. Standing Waves October 26, 2012

37. Standing Wave • A standing wave is a wave which is reflected back and forth between fixed ends (of a string or pipe, for example). • Reflection may be fixed or open-ended. • Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave.

38. Fixed-end standing waves 1st harmonic 2nd harmonic 3rd harmonic

39. Fixed-end standing waves L Fundamental First harmonic  = 2L First Overtone Second harmonic  = L Second Overtone Third harmonic  = 2L/3

40. Open-end standing waves L Fundamental First harmonic  = 2L First Overtone Second harmonic  = L Second Overtone Third harmonic  = 2L/3

41. Mixed standing waves L First harmonic  = 4L Second harmonic  = (4/3)L Third harmonic  = (4/5)L

42. Physics Challenge A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the center, as shown above. The fundamental frequency of vibration of the string is • 1 Hz • 2.5 Hz • 5 Hz • 7.5 Hz • 10 Hz

43. Sample Problem • How long do you need to make an organ pipe that produces a fundamental frequency of middle C (256 Hz)? The speed of the sound in air is 340 m/s. • A) Draw the standing wave for the first harmonic • B) Calculate the pipe length. • C) What is the wavelength and frequency of the 2nd harmonic? Draw the standing wave

44. Sample Problem • How long do you need to make an organ pipe whose fundamental frequency is a middle C (256 Hz)? The pipe is closed on one end, and the speed of sound in air is 340 m/s. • A) Draw the situation. • B) Calculate the pipe length. • C) What is the wavelength and frequency of the 2nd harmonic?

45. Factors of Wave Velocity • Factors which affect wave velocity on a string include: • Mass (inverse) • String length (direct) • Density (inverse) • Tension (direct)

46. Resonance • Resonance occurs when a vibration from one oscillator occurs at a natural frequency for another oscillator. • The first oscillator will cause the second to vibrate.

47. Beats • “Beats is the word physicists use to describe the characteristic loud-soft pattern that characterizes two nearly (but not exactly) matched frequencies. • Musicians call this “being out of tune”.

48. Amplitude Beats as a result of Superposition