Chapter Twenty-Three: Waves

• 23.1 Harmonic Motion• 23.2 Properties of Waves• 23.3 Wave Motion

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23.1 Harmonic motionA. Linear motion

gets us from one place to another.

B. Harmonic motion is motion that repeats over and over.

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Harmonic motion

• A pendulum is a device that swings back and force.

• A cycle is one unit of harmonic motion.

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Oscillators

• An oscillator is a physical system that has repeating cycles or harmonic motion.

• Systems that oscillate move back and forth around a center or equilibrium position.

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Oscillators• A restoring force is any force that

always acts to pull a system back toward equilibrium.

Harmonic motion• Harmonic motion can be fast or slow,

but speed constantly changes during its cycle.

• We use period and frequency to describe how quickly cycles repeat themselves.

• The time for one cycle to occur is called a period.

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Harmonic motion• The frequency is the

number of complete cycles per second.

• Frequency and period are inversely related.

• One cycle per second is called a hertz, abbreviated (Hz).

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Solving Problems

• The period of an oscillator is 2 minutes.

• What is the frequency of this oscillator in hertz?

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Solving Problems

1. Looking for: frequency in hertz

2. Given: period = 2 min

3. Relationships:– 60 s = 1 min

– f = 1/T

4. Solution: f = 1/120 s

f = .008 Hz

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Amplitude• Amplitude describes

the “size” of a cycle.• The amplitude is the

maximum distance the oscillator moves away from its equilibrium position.

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Amplitude

• The amplitude of a water wave is found by measuring the distance between the highest and lowest points on the wave.

• The amplitude is half this distance.

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Amplitude

• Example: A pendulum with an amplitude of 20 degrees swings 20 degrees away from the center in either direction.

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Graphs of harmonic motion

• A graph is a good way to show harmonic motion because you can quickly recognize cycles.

• Graphs of linear motion do not show cycles.

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A wave with an amplitude of 2cm and a period of 1 second.

432101234

0 1 2 3

Exit Card:Label the parts of the transverse wave.•Crest•Trough•Wavelength•Amplitude

Chapter Twenty-Three: Waves

• 23.1 Harmonic Motion• 23.2 Properties of Waves• 23.3 Wave Motion

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23.2 Waves• A wave is an oscillation that travels from

one place to another.• If you poke a floating ball, it oscillates up

and down.• The oscillation spreads outward from

where it started.

What Are Mechanical Waves?

• A wave is a disturbance that travels through matter or empty space.

• Waves transfer energy.  • Some waves travel through matter

called a medium.• Waves are caused by vibrations.

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Vibrations and Waves• All waves are the propagation of

vibrations.• Without a vibration there would be no

sound.• No light.• No TV.• No radio.

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• What does propagation of vibrations mean?

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Waves• When you drop a ball into water,

some of the water is pushed aside and raised by the ball.

Waves• Waves are a

traveling form of energy because they can change motion.

• Waves also carry information, such as sound, pictures, or even numbers.

Frequency, amplitude, and wavelength

• You can think of a wave as a moving series of high points and low points.

• A crest is the high point of the wave.• A trough is the low point.

Frequency

• The frequency of a wave is the rate at which every point on the wave moves up and down.

• Frequency means “how often”.

Amplitude

• The amplitude of a water wave is the maximum height the wave rises above the level surface.

Wavelength• Wavelength is the distance from any point

on a wave to the same point on the next cycle of the wave.

• The distance between one crest and the next crest is a wavelength.

• Answer Questions 1-4

A wave with an amplitude of 1cm and a wavelength of 2 cm. 2

1.51.50.51

1.520 1 2 3 4 5 6 7 8 9

A wave with an amplitude of 1.5cm and a wavelength of 3 cm.

21.5

1.50.51

1.520 1 2 3 4 5 6 7 8 9

The speed of waves• The speed of a water wave is how fast

the wave spreads, NOT how fast the water surface moves up and down or how fast the dropped ball moves in the water.

How do we measure the wave speed?

The speed of waves

• A wave moves one wavelength in each cycle.

• Since a cycle takes one period, the speed of the wave is the wavelength divided by the period.

The speed of waves• The speed is the distance traveled (one

wavelength) divided by the time it takes (one period).

• We usually calculate the speed of a wave by multiplying wavelength by frequency.

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Wave Speed (Velocity)

V= f• The Greek

letteriswavelength.37

Solving Problems

• The wavelength of a wave on a string is 1 meter and its speed is 5 m/s.

• Calculate the frequency and the period of the wave.

Solving Problems

1. Looking for: – frequency in hertz– period in seconds

2. Given– = 1 m; s = 5 m/s

3. Relationships:– s = f x or f = s ÷ – f = 1/T or T = 1/f

4. Solution– f = 5 m/s ÷1 m = 5 cycles/s– T = 1/5 cycles/s = .2 s

f = 5 Hz

T = 0.2 s

A wave in a spring has a wavelength of 1 meters and a period of 2 seconds. What is the speed of the wave?

• Speed = wavelength / period• S = 1 m/ 2 s• S= 0.5 m/s

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What is the speed of an ocean wave that has a wavelength of 4.0 m and a

frequency of 0.5 hz?

• Speed = wavelength x frequency• Speed = 4.0 m x 0.5 hz• Speed = 2 m/s

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Find the wavelength of a wave in a rope that has a frequency of 20 hz and

a speed of 4 m/s.

• Wavelength = speed / frequency• Wavelength = 4 m/s / 20 hz• Wavelength = 0.2 m

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A wave with an amplitude of 3cm and a wavelength of 6 cm. 4321012340 1 2 3 4 5 6 7 8 9

A wave with an amplitude of 4cm and a wavelength of 4 cm. 4321012340 1 2 3 4 5 6 7 8 9

Chapter Twenty-Three: Waves

• 23.1 Harmonic Motion• 23.2 Properties of Waves• 23.3 Wave Motion

23.3 Wave Motion• A wave front is the

leading edge of a moving wave which is considered to be the crest for purposes of modeling.

• The crests of a plane wave look like parallel lines.

• The crests of a circular wave are circles.

Four wave interactions• When a wave encounters a surface, four

interactions can occur:1. reflection,2. refraction, 3. diffraction, 4. absorption.

Wave interactions• A boundary is an edge or surface

where things change.• Reflection, refraction, and diffraction

usually occur at boundaries.

Reflection

• Reflection: Bouncing off a barrier.– Law of Reflection- Where the angle of

incidence equals the angle of reflection.

  Billiards and Mirrors

• A ball bouncing off the bank of a pool table behaves like a light ray reflecting off a mirror.  

• Refraction: Change in direction of a wave due to change in speed.

• The medium effects the wave.  • Window, water, air temp or what ever the

wave is moving through.

Refraction

Understanding Refraction

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Refraction behavior

• Sound travels faster in warm air.

• The wave bends towards the cold air.

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Water on Road Mirage

• There's no water on the road; why does it appear so?

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Dispersion caused by refraction

• When a white ray of light passes through a prism, it will be split into the colors of the spectrum

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Understanding Rainbow Geometry

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Rainbow • Rainbows always face the observer.  As the

observer moves, the rainbow moves. • One can never get to the "pot of gold" at the

end of the rainbow.

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• Rainbows always face the observer.  As the observer moves, the rainbow moves.

• One can never get to the "pot of gold" at the end of the rainbow.

Rainbow

Diffraction

• Diffraction: Bending of a wave as it passes around a corner or thru a small opening.

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Wave interactions

• Diffraction usually changes the direction and shape of the wave.

• When a plane wave passes through a small hole diffraction turns it into a circular wave.

Water Waves Bend around Obstacles

• Waves diffract through an opening. If the wavelength is comparable to the width of opening, significant changes in direction occur.

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Diffraction by Edges of Holes• The smaller the obstacle or opening, the

greater the bending. Bending is greatest when the opening is smallcompared to the wavelength.  

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Transverse and longitudinal waves

• A wave pulse is a short ‘burst’ of a traveling wave.

• It is sometimes easier to see the motion of wave pulses than it is to see long waves with many oscillations.

Transverse waves• The oscillations of a transverse wave

are not in the direction the wave moves.

Transverse

Transverse water wave

Longitudinal waves• The oscillations of a longitudinal wave

are in the same direction that the wave moves.

Longitudinal

Interference• Interference: occurs when two waves meet

and add their amplitudes.

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Constructive interference• Constructive interference happens when

waves add up to make a larger amplitude.• Suppose you make two wave pulses on a

stretched string. • One comes from the left and the other

comes from the right. • When the waves meet, they combine to

make a single large pulse.

Destructive interference

• What happens when one pulse is on top of the string and the other is on the bottom?

• When the pulses meet in the middle, they cancel each other out.

• During destructive interference, waves add up to make a wave with smaller or zero amplitude.