1. General Physics waves_2
Group Work
Add these two waves together.
Demo equipment: coil spring and table clamp; wave tank, bucket, block, plunger, cork floats; corrugated resonance tube

2. General Physics waves_2 Part 2: resonance and more dimensions

3. General Physics waves_2
Objectives
Evaluate combinations of waves from confined systems.
Explain the refraction of waves.
Explain the behavior of ocean waves near the shore.

4. General Physics waves_2
Combinations of Waves

5. General Physics waves_2
Standing Waves
Sum of waves of equal amplitude and wavelength traveling in opposite directions
Half-wavelength divides exactly into the available space
Wave pattern has locations of minimum and maximum variation (nodes and antinodes)
(standing longitudinal waves)
Run at: w1 = 0.2; k1 = 0.2; ampl = 15
integral multiples (half, third, quarter) of lambda: multiply w1, k1 by 2, 3, 4
add same-lambda wave with negative amplitude
Beats: slightly vary w2 and k2 together from wave 1 values (0.22 and 0.22; 0.21 and 0.21, etc.)
Standing waves (use w of about 0.2; try w = 0.2, k = 0.1)

6. General Physics waves_2
Resonance
Objects have characteristic frequencies at which standing waves are sustained
Lowest frequency = fundamental
Higher frequencies = overtones
Sustained motion is a combination of normal modes

7. Vibrational Modes: Clamped String
General Physics waves_2
Vibrational Modes: Clamped String
Insert Figure 15.3 from class text
Source: Griffith, The Physics of Everyday Phenomena, Figure 15.13

8. General Physics waves_2
Poll Question
Bowing a ‘cello string 1/4 of the way along will excite which harmonic the MOST?
The fundamental.
The first overtone.
The second overtone.
The third overtone.
Most energy into antinode of first overtone.

9. Group Work
Add together:
a fundamental and second overtone.

10. General Physics waves_2
Group Work Result
Add together:
a fundamental and first overtone.
Approaching a sawtooth wave

11. General Physics waves_2
Group Work Result
Add together:
a fundamental and second overtone.
Approaching a square wave

12. Combinations of Harmonics
General Physics waves_2
Combinations of Harmonics
Characteristic sounds arise from combining particular harmonics in specific ratios
Fourier analysis suimulation
flute
oboe
saxophone

13. “Closed” and “Open” Tube Modes
General Physics waves_2
“Closed” and “Open” Tube Modes
Source: Halliday, Resnick, and Walker, Fundamentals of Physics, 2003, p 419.

14. General Physics waves_2
Poll Question
Which has the lowest fundamental tone?
A closed tube of length L.
An open tube of length L.
Both have the same fundamental tone.
Not enough information.

15. General Physics waves_2
Sequence of Harmonics
Western musical scale and harmonies are based on overtone series
(sound files)
Sound files: overtones of open tube or clamped string

16. Musical Tones Octave higher = 2 the frequency
Octave + fifth: 3 the frequency
Even-tempered scale = compromise to facilitate transposition
12 (half-) steps per octave
Half-step:  the frequency 12

17. Two-Dimensional Waves
General Physics waves_2
Two-Dimensional Waves
Ocean waves
Earthquake surface waves
Animation rectangular membrane
Animation circular membrane

18. Wave Refraction Direction changes to keep wave front continuous
Source: University of Southampton, Institute for Sound and Vibration Research

19. Wave Refraction Snell’s Law: u2 sinq1 = u1 sinq2 q1 q2 Speed u1

20. Question
Waves approach a slow zone at an angle. The direction the waves travel
does not change.
bends toward the interface.
bends away from the interface. C
slow A B
fast

21. Refraction Example
u = 1/2
u = 3/4
u = 1

22. Water Waves Restoring force is gravity
Fastest in deep water, slow in shallow water
Breaking and refractive behavior in shallow water
Speed depends on wavelength
Very complicated behavior!

23. Question Ocean waves approaching a shore will
bend so that the wave fronts make a greater angle with the shore.
bend so that the wave fronts are more parallel to the shore.
veer away from the shore.
not change their direction.

24. General Physics waves_2
Ocean Wave Refraction

25. Group Work
Sketch how the train of waves would move into the region of slow speed.
fast
slow

26. General Physics waves_2
Breaking Wave

27. Shoaling and Breaking Waves slow in shallows by shore
Wavelength shortens and amplitude rises
Troughs move slower than crests
Crests fall forward

28. Question When waves approach the shore, their increases and decreases.
speed, mass
force, mass
wavelength, period
amplitude, frequency
amplitude, wavelength
frequency, wavelength

29. Tsunami