1. Mechanical Waves
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2. Observations: Pulses and wave motion
When an object vibrates, it also disturbs the medium surrounding it.
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3. Wave motion
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4. Two kinds of waves
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5. Wave Behaviors
**Reflection: wave is reflected at the boundary of the medium it is traveling in.
Fixed Boundary: wave is reflected AND inverted
Free Boundary: wave is reflected
Refraction: wave bends when it travels from one type of medium to another type because the velocity of the wave changes
Transmission: some energy from the wave is reflected and some continues on
Diffraction: wave bends through and opening or around a barrier within the SAME medium
**Interference: when 2 waves interfere with each other (could be constructive or destructive)

6. Fixed end reflection Free end reflection
Animations courtesy of Dr. Dan Russell, Kettering University
Fixed end reflection
Free end reflection

7. Some energy reflected and some transmitted.
Boundary Behavior in Transmission
Transmission—wave passing from one medium to another
Some energy reflected and some transmitted.
less dense to more dense
v2 < v1
* Reflected pulse is inverted
more dense to less dense
v2 > v1
*Reflected pulse same orientation as incident wave
Animations courtesy of Dr. Dan Russell, Kettering University

8. Impedance
Impedance characterizes the degree to which waves are reflected and transmitted at the boundary between different media.
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9. Ultrasound
Ultrasound takes advantage of the differing densities of internal structures to "see" inside the body.
The impedance of tissue is much greater than that of air. As a result, most of the ultrasound energy is reflected at the air-body interface and does not travel inside the body.
To overcome this problem, the area of the body to be scanned is covered with a gel that helps "match" the impedance between the emitter and the body surface.
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10. Interference
- Occurs when two or more waves meet while traveling along the same medium.
- May be constructive or destructive

11. Constructive Interference1m 2m 1m

12. Constructive Interference
When 2 or more waves are in phase with each other they will “construct” a bigger wave at the instant they are interfering with each other

13. Destructive Interference1m 1m

14. Destructive Interference
When 2 or more waves are out of phase with each other they will “destruct” at the instant they are interfering with each other

15. Incomplete Destructive Interference

16. It is not always a complete construction or destruction!

17. Something to remember!
Waves continue to move passed each other after they have interfered, even after “destructing”
Think of it as instantaneously destructing

18. Stop and work on the Wave interference side of the WS

19. Sound waves If you strike a tuning fork, you hear sound.
You can feel the vibrations of the prongs if you touch them.
If you place the vibrating prongs in water, you see ripples going out.
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20. Wavelength
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21. Phase
Two points in a medium are "in phase" if at every clock reading, their displacements are exactly the same.
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22. For Mechanical Waves…
Higher Amplitude = Higher Energy

23. Amplitude in Transverse and Longitudinal Waves
Compressions and rarefactions more pronounced

24. Wave amplitude and energy in a two-dimensional medium
A beach ball bobs up and down in water in simple harmonic motion, producing circular waves that travel outward across the water surface in all directions.
The amplitudes of the crests decrease as the waves move farther from the source.
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25. Wave power and wave intensity
The intensity of a wave is defined as the energy per unit area per unit time interval that crosses perpendicular to an area in the medium through which it travels:
The unit of intensity I is equivalent to joules per second per square meter or watts per square meter.

26. Sound
We hear sound when pressure variations at the eardrum cause it to vibrate.
Pressure waves in the frequency range that we can hear are called sound.
Higher- or lower-frequency pressure waves are called ultrasound or infrasound.
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27. Loudness and intensity
Loudness is determined primarily by the amplitude of the sound wave: the larger the amplitude, the louder the sound.
Equal-amplitude sound waves of different frequencies will not have the same perceived loudness to humans.
To measure the loudness of a sound, we measure the intensity
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28. Intensities and intensity levels of common sounds
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29. Pitch, frequency, and complex sounds
Pitch is the perception of the frequency of a sound.
Tuning forks of different sizes produce sounds of approximately the same intensity, but we hear each as having a different pitch.
The shorter the length of the tuning fork, the higher the frequency and the higher the pitch.
Like loudness, pitch is not a physical quantity but rather a subjective impression.
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30. The Doppler effect: Putting it all together
When you hear the sound from a horn of a passing car, its pitch is noticeably higher than normal as it approaches, but noticeably lower than normal as it moves away.
This phenomenon is an example of the Doppler effect.
The Doppler effect occurs when a source of sound and an observer move with respect to each other and/or with respect to the medium in which the sound travels.
The observer will perceive to hear the sound at a different pitch than the pitch the sound is actually emitting (the pitch of the sound is not actually changing… it’s perception!)

31. Doppler effect for the source moving relative to the medium
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32. Stop work on the Doppler side of the WS and finish Harmonics tomorrow
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33. Fundamental and harmonics
The lowest frequency of a complex wave is called the fundamental.
Higher-frequency components that are whole-number multiples of the fundamental are called harmonics.
We usually identify the pitch as the fundamental frequency.
The complexity of the waveform (the number of harmonics) contributes to the quality of the sound we associate with specific instruments.
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34. Beat and beat frequencies
Two sound sources of similar (but not the same) frequency are equidistant from a microphone that records the air pressure variations due to the two sound sources as a function of time.
This is a Beat.
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35. Beat and beat frequencies
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36. Standing waves on strings
You shake the end of a rope that is attached to a fixed support.
At specific frequencies, you notice that the rope has large-amplitude sine-shaped vibrations that appear not to be traveling.
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37. Standing wave frequencies on a string (Cont'd)
Or first harmonic
Or second overtone
Or third overtone
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38. Standing waves on a string
In a standing wave, only the antinodes reach the maximum displacement.
The nodes do not vibrate at all.
All of the points vibrate in phase.
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39. String with strobe light
Standing wave demos
Long spring
String with strobe light
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40. Harmonics vibrate differently based on the boundaries!
Closed-Closed boundary
Harmonics will only have resonant frequencies that are whole number multiples of the fundamental frequency

41. Harmonics vibrate differently based on the boundaries!
Open-Open boundary
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42. Harmonics vibrate differently based on the boundaries!
Open-Closed boundary
Does this boundary scenario produce a 2nd harmonic?
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43. Exciting the sound and changing the pitch of a wind instrument
In clarinets and saxophones, the sources of vibrations are the reeds. In trumpets, trombones, and French horns, the sources of vibrations are the vibrating lips and mouthpiece.
The vibrations produced by the reeds and mouthpieces are pressure pulses at a variety of frequencies.
The pipes attached to the reeds and mouthpieces reinforce only those input frequency vibrations that are at resonant frequencies of the instruments.
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