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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

Where do we encounter waves? Write down all the examples of waves that you can think of

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Page 1: Where do we encounter waves? Write down all the examples of waves that you can think of

Where do we encounter waves? Write down all the examples of waves that you can think of.

Warm-Up: January 30, 2012

Page 2: Where do we encounter waves? Write down all the examples of waves that you can think of

Vibrations and WavesChapter 14

Page 3: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 4: Where do we encounter waves? Write down all the examples of waves that you can think of

Periodic Motion Graph

x

Page 5: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 6: Where do we encounter waves? Write down all the examples of waves that you can think of

How much force is needed to stretch a spring 25 cm if the spring constant is 105 N/m?

Example 1

Page 7: Where do we encounter waves? Write down all the examples of waves that you can think of

How much force is needed to compress a spring 12 cm if the spring constant is 84 N/m?

You-Try #1

Page 8: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 9: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 10: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 11: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 12: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 13: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 14: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 15: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 16: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 17: Where do we encounter waves? Write down all the examples of waves that you can think of

Identify which point(s) correspond with each of the following: crest, trough, amplitude, wavelength

Think, Pair, Share

Page 18: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 19: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 20: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 21: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 22: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 23: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 24: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 25: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 26: Where do we encounter waves? Write down all the examples of waves that you can think of

The following are all used to measure and/or describe waves:

Wave Speed Amplitude Period Frequency Wavelength

Measuring Waves

Page 27: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 28: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 29: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 30: Where do we encounter waves? Write down all the examples of waves that you can think of

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:

Page 31: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 32: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 33: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 34: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 35: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 36: Where do we encounter waves? Write down all the examples of waves that you can think of

Homework Questions?

Page 37: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 38: Where do we encounter waves? Write down all the examples of waves that you can think of

Superposition Examples

Page 39: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 40: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 41: Where do we encounter waves? Write down all the examples of waves that you can think of

Stringed instruments depend on standing waves to make music.

These standing waves are called harmonics.

Standing Waves in Music

Page 42: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 43: Where do we encounter waves? Write down all the examples of waves that you can think of

Homework Questions?

Page 44: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 45: Where do we encounter waves? Write down all the examples of waves that you can think of

The law of reflection states that the angle of incidence equals the angle of reflection

Reflection of 2-D Waves

Page 46: Where do we encounter waves? Write down all the examples of waves that you can think of

Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71, 72, 76, 79, 81

Assignment

Page 47: Where do we encounter waves? Write down all the examples of waves that you can think of

Read Conceptual Physics chapter 25 (pages 372-386)

Answer review questions #1-20 on p. 387-388

Classwork

Page 48: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 49: Where do we encounter waves? Write down all the examples of waves that you can think of

1. energy2. matter3. transverse4. longitudinal5. surface6. transverse7. energy, formation8. speed, wavelength

Waves Worksheet Answers

Page 50: Where do we encounter waves? Write down all the examples of waves that you can think of

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

Page 51: Where do we encounter waves? Write down all the examples of waves that you can think of

Waves Worksheet Answers

smv

m

m

sT

HzF

48)16

9.9)15

3.2)14

1000.8)13

260)123

Page 52: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 53: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 54: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 55: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 56: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 57: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 58: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 59: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 60: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 61: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 62: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 63: Where do we encounter waves? Write down all the examples of waves that you can think of
Page 64: Where do we encounter waves? Write down all the examples of waves that you can think of

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