1. Foundations of Physical Science
Unit 4: Sound and Waves

2. Chapter 12: Waves 12.1 Waves 12.2 Waves in Motion
12.3 Natural Frequency and Resonance

3. Learning Goals
Learn the role waves play in our daily lives, including our effort to communicate.
Learn the parts and shapes of waves.
Model transverse and longitudinal waves and their characteristics with a stretched string.
Explore the properties of waves (like reflection and diffraction) with water.
Investigate resonance and harmony using an electronic synthesizer.
Learn how natural frequency and resonance are involved in making music.

4. Vocabulary circular waves continuous harmonics
constructive interference
crest hertz
destructive interference
diffraction
fundamental plane
longitudinal wave
natural frequency
reflection
refraction
resonance
response
transverse wave
trough
standing wave
wave fronts
waves

5. Why learn about waves?
Waves carry information and energy over great distances
Anytime you see a vibration that moves
Sound waves
Radio waves
Microwaves
The information could be sound, color, pictures, commands, or many other useful things

6. Transverse Waves
The direction of the wave travel is perpendicular to the direction of the vibrating source
Examples:
Stringed instruments
Water waves
Electromagnetic waves

7. Longitudinal Waves
The direction of the wave is along the direction in which the source vibrates
Example:
Shake a slinky back and forth

8. Frequency, Amplitude, & Wavelength
Waves have cycles, frequency, and amplitude, just like oscillations
Frequency: how often the wave goes up and down; measured in hertz
Amplitude: the largest amount that goes above or below average; ½ distance between the highest and lowest places

9. Frequency, Amplitude, & Wavelength
Wavelength: the length of one complete cycle of a wave
Crest-to-Crest
Trough-to-Trough
Represented by lambda λ

10. Wave Speed
How fast the wave can transmit an oscillation from one place to another
Water waves are slow; a few mph
Sound waves are fast; 660 mph
Light waves are very fast; 186,000 mph
How quickly a movement of one part of the water surface is transmitted to another place
Start a ripple in one place and measure how long it takes the ripple to affect a place some distance away

11. Wave Speed Wave speed = wavelength/period
Wave speed = wavelength X frequency
The speed of a wave is related to the frequency and wavelength of the waves
Example: wavelength =10 m
Time between crests at a point on the surface = 0.5 s
The wave moves 10 m / 0.5 s, or 20 m/s

12. Wave Speed
In one complete cycle, a wave moves forward one wavelength

13. Example
If a water wave vibrates up and down 3 times each second and the distance between wave crests is 2m, what is the:
(a) wave’s frequency?
(b) wavelength?
(c) wave speed?
(a) 3 Hz
(b) 2m
(c) wave speed = frequency x wavelength = 3/s x 2 m = 6 m/s

14. Wave Shapes Crest: the highest points of the wave
Wave fronts: another name for the crests of the wave
Wave shapes are determined by the wave fronts
Trough: the lowest points of the wave

15. Wave Shapes
Plane waves: the crests look like straight lines; waves move in a line perpendicular to the wave fronts
Circular waves: the crests are circles; waves move outward from the center

16. What Happens When A Wave Hits Something?
Reflection
Refraction
Diffraction
Absorption
Boundaries: waves are affected by boundaries where conditions change

17. Natural Frequency
A frequency at which an elastic object naturally tends to vibrate
Minimum energy is required to produce a forced vibration or to continue vibration at that frequency

18. Natural Frequency
The natural frequency depends on many factors, such as tightness, length, or weight of a string
We can change the natural frequency of a system by changing any of the factors that affect the size, inertia, or forces in the system
Tuning guitar changes the natural frequency of a string by changing its tension

19. Natural Frequency
All things in the universe have a natural frequency, and many things have more than one.
If you know an object’s natural frequency, you know how it will vibrate.
If you know how an object vibrates, you know what kinds of waves it will create.
If you want to make specific kinds of waves, you need to create objects with natural frequencies that match the waves you want

20. Resonance
The natural frequency of the system exactly in tune with the force applied
Something is vibrated at its natural frequency

21. Resonance Examples
Calvary troops marching across a footbridge in England in 1831 caused a bridge to collapse when they marched in rhythm with the bridge’s natural frequency! Troops must “break step” when crossing bridges
1940 collapse of the bridge across the Tacoma Narrows in Washington
Four months after being built the bridge was destroyed by wind-generated resonance

22. Standing Waves A stationary wave pattern formed in a medium
Two sets of identical waves pass through the medium in opposite directions
The effect of waves passing through each other

23. Standing Waves
Positions of zero rope displacement in a standing wave are called nodes
At each end of any loop there is a node, and two loops make one wavelength
Distance between adjacent nodes is one-half wavelength

24. Standing Waves on a String
A wave trapped in one spot
A vibrating string; makes music on a guitar or piano
Standing waves occur at frequencies that are multiples of the fundamental
Fundamental: the natural frequency of the string
Harmonics: the fundamental and multiples of its frequencies

25. Standing Waves on a String
A vibrating string moves so fast that your eye averages out the image and sees a wave-shaped blur
We can control standing wave frequencies and wavelengths
We can increase amplitude

26. Interference
The result of superimposing two or more waves of the same wavelength

27. Interference
Constructive Interference: occurs when waves add up to make a larger amplitude
Destructive Interference: occurs when waves add up to make a smaller amplitude

28. Constructive Interference
Crest-to-crest reinforcement

29. Destructive Interference
Crest-to-trough cancellation

30. Example
Is it possible for one wave to cancel another so that no amplitude remains?
Yes. This is destructive interference.
In a standing wave in a rope, for example, parts of the rope-the nodes-have no amplitude because of destructive interference.