Waves and Sound

1. Waves and Sound Animations courtesy of Dr. Dan Russell, Kettering University

2. Simple Harmonic Motion

3. At rest, the mass is at its equilibrium position • If displaced and released from the equilibrium position, it will vibrate about the equilibrium position • This is known as simple harmonic motion • Any object vibrating about an equilibrium position is undergoing simple harmonic motion

4. Describing Harmonic motion • Amplitude (A) – maximum displacement from equilibrium (units: meters) • Period (T) – amount of time elapsed after 1 complete vibration (or cycle) (units: seconds) • Frequency (f) – how many cycles completed in 1 second (units: cycles/ second or Hertz)

5. The Mathematical Relationship Between Period and Frequency • They are inverse quantities f = 1 / T (Hz) T = 1 / f (s)

6. Waves • Waves are generated by harmonic motion • Waves require a medium to travel through • A medium is any solid, liquid, or gas • Waves represent the transfer of energy through a medium • Wave pulse animation

7. Longitudinal and Transverse waves • When a waves travel through a medium, the particles of the medium vibrate • Longitudinal wave – particles of the medium vibrate parallel to the direction that the wave is traveling • Transverse wave – particles of the medium vibrate perpendicular to the direction that the wave is traveling • Wave animations

8. Describing waves • Since harmonic motion generates waves, the same terms are used to describe both • Amplitude – height of the wave (units: meters) • Frequency – how many waves pass you each second (units: waves per second or Hertz) • Period – amount of time that elapses between each successive wave (units: seconds) • Wavelength – distance between waves (units: meters)

9. Describing waves

10. The velocity of a Wave • Velocity of a wave = wavelength x frequency (units: m/s) • This equation applies to all waves v = λ f

11. Sound • Sound waves are longitudinal waves • The speed of sound depends on the air temperature • It increases by 0.6 m/s for each degree Celsius above 0 oC

12. The Speed of Sound • The formula for the speed of sound at a certain air temperature: S = 331m/s + (0.6m/s/oC)T • S = speed of sound • T = temperature • This formula is accurate between 0-100oC

14. Wavefronts • Sound waves spread from their source as spherical waves • Each successive wave is called a wavefront • Animation

15. Wavefronts become linear far from the source

16. Reflection • When a wavefront encounters a boundary between two mediums, reflection occurs • An echo is an example of sound being reflected • SONAR uses reflection of waves to locate objects under water • Part of the wave is transmitted to the other medium

18. Refraction • Refraction – when a wave changes direction • Causes: • A wave travels from one medium into another • Ex: Sound traveling from air into water • When a wave encounters different conditions within a medium • Ex: Sound traveling into air of a different temperature

19. Refraction The direction of the wavefront changes because of the temperature difference in the air

20. Refraction Refraction animation

21. The Principle of Superposition: Interference • When two waves cross, another wave is created which is the sum of the two individual waves • Interference animation • This is known as the principle of superposition • The Principle of Superposition results in what is called interference • There are two types of interference: • Constructive • Destructive

22. Constructive Interference

23. Destructive Interference

24. Beat Frequencies • Imagine 2 sources generating waves of slightly different frequencies • Interference will cause what is known as a beat frequency • The beat frequency equals the difference between the source frequencies fb = f2 – f1

25. Beat Frequencies

26. Vibrating Strings and Standing Waves • When a transverse wave reaches a boundary, the reflected wave is inverted • Reflection animation • Reflected waves interfering with incoming waves of the same frequency produce standing waves • Standing wave animation • Standing wave animation 2

27. The speed of a wave on a string • The speed of a wave on a string depends on the tension of the string, and the mass per unit length of the string • It is given by the following formula:

28. Resonance • All material objects have a natural frequencies of vibration (harmonic frequencies) • When the frequency of an applied force on an object matches a harmonic frequency, energy is transferred very efficiently • This is known as resonance • During resonance, the amplitude of vibration becomes very high • The harmonic frequencies of a vibrating string and an open tube are examples of resonance and are also called resonant frequencies

29. Videos • Wine Glass • Tacoma Narrows bridge

30. Harmonics • Consider a string tied down at both ends • It will only vibrate at certain frequencies • The resonant or natural frequencies of vibration • These are also known as harmonic frequencies

31. The fundamental frequency of a vibrating string

32. The string will also vibrate at frequencies that are integer multiples of the fundamental frequency • These are known as Harmonic frequencies • Harmonic frequencies produce standing waves

34. The Doppler effect • The frequency of a sound wave will change if the source of the sound is moving relative to you • If the source is moving towards you, the frequency increases • If the source is moving away from you, the frequency decreases • This is known as the Doppler effect

35. Stationary Source

36. Moving source

37. Videos • Listener in motion • Car horn

38. Interference and standing waves • http://www.youtube.com/watch?v=tI6S5CS-6JI&NR=1 • Water • http://www.youtube.com/watch?v=LCk9-blM5Xg&feature=related • Cornstarch • http://www.youtube.com/watch?v=4shodbQMcmM&NR=1 • Faraday waves • http://www.youtube.com/watch?v=Yw4qklgNIxI&feature=related • Speakers • http://www.youtube.com/watch?v=nO0bSSXmr1A • rice

39. Breeching the sound barrier