1. SCI 340 L39 Wave interference
Combining Waves
Ch. 17

2. SCI 340 L39 Wave interference
Group Work
Sketch the wave resulting from the addition of the two waves shown at one instant. 3 –3

3. SCI 340 L39 Wave interference
Group Work
Sketch the wave resulting from the addition of the two waves shown at one instant. 3
result –3

4. SCI 340 L39 Wave interference
Constructive: Sum of waves has increased amplitude
Destructive: Sum of waves has decreased amplitude
Two-wave simulation (not functional)
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)

5. SCI 340 L39 Wave interference
Diffraction
§ 17.3

6. SCI 340 L39 Wave interference
Objectives
Use Huygens’s principle to explain why diffraction occurs.
Describe the diffraction of waves around barriers.

7. SCI 340 L39 Wave interference
Diffraction
A wave front passing through a barrier bends at the edges
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)

8. Understanding Diffraction
SCI 340 L39 Wave interference
Understanding Diffraction
Huygens’s Principle: A wave front is composed of “wavelets”

9. Understanding Diffraction
SCI 340 L39 Wave interference
Understanding Diffraction
Huygens’s Principle: A wave front is composed of “wavelets”
that interfere to produce the observed front

10. Single Slit Diffraction
SCI 340 L39 Wave interference
Single Slit Diffraction
Plane waves encounter a slit in a barrier
And diffract as they pass through

11. SCI 340 L39 Wave interference
Diffraction
Wavelets interfere to make nodes and antinodes
(ripple tank simulation)
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)

12. SCI 340 L39 Wave interference
Where are the Nodes?
First minimum (node) at the angle where wave front cancels ½ slit across
Half cycle out of phase
Destructive interference
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)
Reach the detector at the same time D l

13. First Node Rectangular slit: sin q = l/D
Circular aperture: sin q = 1.22 l/D
Most energy is between the first nodes
A narrow aperture makes a wider dispersion
Maximum (sin q) = 1
no nodes if D < l

14. SCI 340 L39 Wave interference
Beats
§ 17.4

15. SCI 340 L39 Wave interference
Beats
Waves of similar frequency combine to give alternating times of constructive and destructive interference
Distinctive “waa-waa” sound with beat frequency equal to the difference in frequency of the component waves (Why?)
(sound files)

16. Standing Waves
Interference in place
§ 17.5–17.6

17. SCI 340 L39 Wave interference
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)

18. SCI 340 L39 Wave interference
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

19. Vibrational Modes: Clamped String
SCI 340 L39 Wave interference
Vibrational Modes: Clamped String
Insert Figure 15.3 from class text
Source: Griffith, The Physics of Everyday Phenomena, Figure 15.13

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

21. SCI 340 L39 Wave interference
Group Work Result
Add together:
a fundamental and first overtone.
Approaching a sawtooth wave

22. SCI 340 L39 Wave interference
Group Work Result
Add together:
a fundamental and second overtone.
Approaching a square wave

23. Combinations of Harmonics
SCI 340 L39 Wave interference
Combinations of Harmonics
Characteristic sounds arise from combining particular harmonics in specific ratios
Fourier analysis suimulation
flute
oboe
saxophone

24. “Closed” and “Open” Tube Modes
SCI 340 L39 Wave interference
“Closed” and “Open” Tube Modes
Source: Halliday, Resnick, and Walker, Fundamentals of Physics, 2003, p 419.

25. SCI 340 L39 Wave interference
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.

26. SCI 340 L39 Wave interference
Sequence of Harmonics
Western musical scale and harmonies are based on overtone series
(sound files)
Sound files: overtones of open tube or clamped string

27. 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

28. Two-Dimensional Waves
SCI 340 L39 Wave interference
Two-Dimensional Waves
Ocean waves
Earthquake surface waves
Animation rectangular membrane
Animation circular membrane