1. Waves and Sound
PHYS 1090 Unit 7

2. Features of a Wave crest trough Crest: high point Trough: low point
Wavelength: crest-crest distance (m)
crest
Period: crest-crest-timing (s)
Here we define names for wave features so that we can communicate easily. l
trough

3. Features of a Wave Amplitude A: (crest height – trough height) / 2
Frequency f: repeats in a given time (cyc/s = Hz)
Velocity u: speed of crest motion (m/s)
Here we define names for wave features so that we can communicate easily. u A

4. Relations between Features
Period T = 1 / f ; Frequency f = 1 / T
Velocity u = l / T
= lf
Wavelength l = uT = u / f
Frequency f = u / l; Period T = l / u

5. Types of Waves
Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave)
Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave)
Animation
Crest and trough of a longitudinal wave: moving regions of highest and lowest pressure or density. Amplitude of a longitudinal wave: Half the total change in pressure or density

6. Combining Waves

7. Adding Waves Together result 3 –3
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
Standing waves (use phase velocity of 0.5: k = 2*w)
result –3

8. Wave Interference Constructive: Sum of waves has increased amplitude
Destructive: Sum of waves has decreased amplitude
Two-wave simulation

9. Beats
Waves of similar frequency combine to give alternating times of constructive and destructive interference

10. Standing Waves
Add a wave to an identical wave traveling in the opposite direction
(Its reflection)
Medium vibrates, but waves don’t travel
Nodes: positions of zero variation
Antinodes: positions of maximum variation

11. Two-Dimensional Waves
Ocean waves, earthquake surface waves
Wave types animations
Membrane standing waves animations

12. 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!

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

14. Wave refraction
u = 1/2
u = 3/4
u = 1

15. Ocean Wave Refraction

16. 2-D Wave Interference interference patterns