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Where do we encounter waves? Write down all the examples of waves that you can think of.
Warm-Up: January 30, 2012
Vibrations and WavesChapter 14
A periodic motion repeats in a regular cycle.
Examples include:◦ Pendulums (such as on a grandfather clock)◦ A mass at the end of a spring◦ Vibrating guitar string
The period is the amount of time for one complete cycle.
The amplitude is the maximum amount that the object moves from its initial, equilibrium position
Periodic Motion
Periodic Motion Graph
x
When you stretch or compress a spring, the spring exerts a force to return it to its equilibrium position.
The amount of force is given by Hooke’s Law
where k is the spring constant (a property of the individual spring)
and x is the distance the spring is from its equilibrium position
Springs
kxFsp
How much force is needed to stretch a spring 25 cm if the spring constant is 105 N/m?
Example 1
How much force is needed to compress a spring 12 cm if the spring constant is 84 N/m?
You-Try #1
Stretching or compressing a spring also generates elastic potential energy
This is a different type of potential energy than the gravitational potential energy we’ve discussed
Energy of Springs
2
2
1kxPEsp
A spring has a spring constant of 256 N/m. How far must it be stretched to give it an elastic potential energy of 48 J?
Example 2
A spring with a spring constant of 144 N/m is compressed by a distance of 16.5 cm. How much elastic potential energy is stored in the spring?
You-Try #2
Resonance occurs when small forces are applied at regular intervals to an object in periodic motion causing the amplitude to increase.
Examples include:◦ Pushing someone on a swing◦ Jumping on a diving board◦ Wind on the Tacoma Narrows Bridge
Resonance
A spring has a spring constant of 125 N/m. It is attached to the ceiling and a block is attached to the bottom. The spring is stretched 20.0 cm.
1) Draw a free body diagram of the block.2) What force does the spring exert on the mass?3) What is the weight of the block?4) What is the elastic potential energy stored in
the spring?
Warm-Up: January 31, 2012
A wave is a disturbance that carries energy through matter or space
A wave usually does NOT transfer mass, only energy
A wave pulse is a single bump or disturbance. Most waves are a series of wave pulses.
Two main types of waves:◦ Mechanical waves – travel through matter◦ Electromagnetic waves – do not require matter,
can travel through a vacuum
Waves
Examples include:◦ Water waves◦ Sound waves◦ Waves on a rope◦ Waves on a spring
Mechanical waves require a medium (matter) through which they propagate (travel).
Three main categories:◦ Transverse Waves◦ Longitudinal Waves◦ Surface Waves
Mechanical Waves
A transverse wave is one that vibrates perpendicular to the direction of the wave’s motion
A wave on a rope is an example of a transverse wave
Simulation
Transverse Waves
Crest – The highest point Trough – The lowest point Amplitude – The maximum displacement
of of the wave◦ The higher the amplitude, the greater the amount
of energy transferred. Wavelength – The distance between crests
(or the distance between troughs)
Parts of a Transverse Wave
Identify which point(s) correspond with each of the following: crest, trough, amplitude, wavelength
Think, Pair, Share
A longitudinal wave is one whose disturbances are in the same direction as (parallel to) the direction of the wave’s motion
Sound waves are longitudinal Waves from a compressed
spring are longitudinal
Longitudinal Waves
Compression – A dense part of a longitudinal wave
Rarefaction – A low density part of a longitudinal wave
Wavelength – The distance between compressions (or the distance between rarefactions)
Parts of a Longitudinal Wave
A man with a mass of 75 kg hangs from a spring that is attached to the ceiling, causing it to stretch 83 cm (after the oscillations stop). What is the spring constant of the spring?
Warm-Up: February 1, 2012
Surface waves are waves with characteristics of both transverse and longitudinal waves.
Ocean waves are a prime example of surface waves.
The paths of individual particles are circular.
Surface Waves
The following are all used to measure and/or describe waves:
Wave Speed Amplitude Period Frequency Wavelength
Measuring Waves
Wave Speed – The distance a wave travels per unit time
Represented by a lower case v Measured in meters per second, m/s Depends on the medium through which the
wave is travelling
Wave Speed
Tt
dv
Amplitude – The maximum displacement of a wave from its at-rest position
Represented by a capital A Measured in meters, m Depends on how the wave was generated Does not depend on the wave speed or the
medium More work must be done to generate larger
amplitude waves. Waves with larger amplitudes transfer more
energy
Amplitude
Period - the amount of time for one complete cycle/oscillation
Represented by a capital T Measured in seconds Depends only on the wave source Does not depend on the wave speed Does not depend on the medium
Period
Frequency – The amount of cycles/oscillations per second
Represented by a lower case f Measured in Hertz, Hz Depends only on the wave source Does not depend on the wave speed Does not depend on the medium
Frequency
Tf
1
sHzunits
1:
Wavelength – Length of a cycle (distance between similar points)
Distance between crests (or troughs) of a transverse wave
Distance between compressions (or rarefactions) of a longitudinal wave
Represented by Greek letter lambda, λ Measured in meters
Wavelength
vTf
v
Sound waves travel approximately 340 m/s in air. What is the wavelength of a sound wave that has a frequency of 170 Hz?
Example 3
2.0 m
Sound has a speed of 3100 m/s in copper. What is the wavelength of the wave from Example 3 after it crosses into a copper medium?
You-Try #3
18 m
What happens when a wave reaches the end of its medium?
When the incident wave reaches the end of its medium, some or all of the energy is reflected back as a reflected wave.
Some reflected waves are inverted, such as waves on a rope with a fixed end (as in the simulation)
Wave Reflection
A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
1) What is the speed of the clock’s chime in air?2) If the sound wave has a frequency of 436 Hz,
what is the period of the wave?3) What is the wave’s wavelength?
Warm-Up: February 6, 2012
Homework Questions?
The principle of superposition states that the amplitude of passing wave pulses is additive.
If pulses are on opposite sides, one amplitude is negative (adding a negative subtracting)
The result of superposition is called interference.
Superposition
Superposition Examples
Interference can cause standing waves, which appear to not propagate.
Example: Rope moves up and down, but no wave pulses move to either side.
The nodes are points that do not move. The antinodes are the points that move
the most.
Simulation: Amplitude=20, Frequency=30, Damping=0, Tension=high-1
Standing Waves
Stringed instruments depend on standing waves to make music.
These standing waves are called harmonics.
Standing Waves in Music
A wave has a frequency of 225 Hz. What is its period?
The wave changes medium from air to water. What happens to the period? (increase, remain constant, or decrease)
Warm-Up: February 7, 2012
Homework Questions?
Often represented by a wave front, a line that represents a wave crest.
Waves move perpendicular to the wave front, often represented by a ray.
Waves in Two Dimensions
The law of reflection states that the angle of incidence equals the angle of reflection
Reflection of 2-D Waves
Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71, 72, 76, 79, 81
Assignment
Read Conceptual Physics chapter 25 (pages 372-386)
Answer review questions #1-20 on p. 387-388
Classwork
List the five characteristics that are used to measure/describe waves.
Which of the above depend on the medium through which the wave is travelling?
Warm-Up: February 13, 2012
1. energy2. matter3. transverse4. longitudinal5. surface6. transverse7. energy, formation8. speed, wavelength
Waves Worksheet Answers
9. The speed of a wave is equal to its wavelength divided by its period.
10. If the frequency of a wave decreases while wave speed remains constant, the wavelength increases.
11. The wavelength of a longitudinal wave is the distance between compressions (or rarefactions). The wavelength of a transverse wave is the distance between crests (or troughs).
Waves Worksheet Answers
Waves Worksheet Answers
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m
m
sT
HzF
48)16
9.9)15
3.2)14
1000.8)13
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