Simple Harmonic Motion and Waves

What is common between the following?

• Acrobat swinging on a trapeze

• Child swinging on a swing

• Pendulum of a grandfather clock

• A wrecking ball swinging back and forth.

SIMPLE HARMONIC MOTION

The back and forth vibrating motion (often called oscillatory motion) of an object. A graph of this motion is a sine curve.

SIMPLE HARMONIC MOTIONOF A MASS ATTACHED TO A

SPRING

SPRING SIMPLE HARMONIC MOTION ANIMATION

http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/SHM/TwoSHM.html

What is a wave?

A wave is a wiggle in space

and time is caused by a

vibration carries energy not

matter

Mechanical and Electromagnetic

1st Major Category

Mechanical Waveswaves that require a medium (solid, liquid, or

gas) through which to travel.Speed of the waves depends on the elasticity of

the mediumAre governed by Newton’s Laws3 types of mechanical waves: transverse,

longitudinal, and surface

Types of mechanical waves

• Transverse wave- particle displacement is perpendicular to the wave motion

• Examples include waves in piano and guitar strings

Types of mechanical waves (cont)

• Longitudinal waves- particle displacement is parallel to the wave motion

• Sound is a longitudinal wave

• Fluids, liquids, gases, and plasmas usually only transmit longitudinal waves

Types of mechanical waves (cont)

• Surface waves- a combination of both transverse and longitudinal waves

• Waves on the water’s surface are examples of surface waves

Properties of mechanical waves*

1. Crest- the high point of a wave

2. Trough- the low point of a wave

3. Amplitude- measurement of the amount of energy the wave carries

*Some properties are only found in transverse waves and some properties are only found in longitudinal waves.

Properties of mechanical waves* (cont)

4. Wavelength- the distance between the midpoint of one crest/trough to the midpoint of the next crest/trough

Compression – In longitudinal waves, sections of shorter wavelength

Rarefaction – In longitudinal waves, sections of longer wavelength

5. Line of equilibrium- the resting point of a wave

Concept Check: Label the crest, trough, wavelength, amplitude, and line of

equilibrium on the transverse wave.

Check your answer!

Concept Check: On the given longitudinal wave, label the compression, rarefaction, and

wavelength.

Check your answer!

Velocity of mechanical waves

• Calculated using the formula

• V = fλ

• Where v is velocity, f is frequency, and λ is wavelength.

Period and Frequency of Waves• Period (T) is amount of time for one cycle

T = 1/f

• Frequency (f) is how many waves pass in one second.

f = 1/T

Relationship between these variables is inverse….

As frequency of waves increases the period of a single wave decreases.

Solve the following problem

• Problem: Calculate the velocity of waves in water that are 0.4 m apart and have a frequency of 2 Hz.

• Answer: v = fλ

v = (2 Hz)(0.4 m)

v = 0.8 m/s

Again….

• Problem: What is the wavelength of a 340 Hz sound if the velocity of sound is 343 m/s?

• Answer: v = fλ

343 m/s = (340 Hz)λ

1.0 m = λ

A Little More Practice

• A speaker vibrates at a frequency of 200 Hz. What is its period?

T = 1/f 1/200Hz = .005 sec

What does .005 sec mean in words?

• A swing has a period of 10 seconds. What is its frequency?

F = 1/T 1/10sec = .1 Hz

Wave Interference

• Waves have a very unique property, they can occupy the same space at the same time.

• This phenomenon is called interference!

• Interference can be either constructive or destructive.

Wave Interference (Cont)

• Constructive interference, or reinforcement, occurs when the crests of two waves overlap each other and the amplitudes are added together.

Wave Interference (cont)

• Destructive interference, or cancellation, occurs when a crest and a trough of two waves overlap and their amplitudes cancel out.

WavesWavesdo not move or carry

include examples

such as

transfer energy

through

includes

transfer or carry

mechanical waves

can be classified into two

categories

transverse waves

move move

to transfer

do not requir

e

include examples

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are further classified into

are a special type of

Simple Harmonic Motion and Waves

Part 2

Day One Review

• What are the two types of waves?• Waves must move either parallel or

________________ to the movement of energy.

• The point of the wave that is furthest away from the resting line is the __________________.

• The ______________________ measures the amount of energy in the wave.

2nd Major Category

• Electromagnetic wavesWave does not need a medium to travelWave that is partly electric and partly

magneticAll EM waves are located on the

electromagnetic spectrumAll EM waves travel at the speed of light

(3.0 x 108 m/s)

The Electromagnetic Spectrum

Solving an EM problem

• The velocity for all EM waves is 3.0 x 108

m/s and is represented by the letter c.

• Therefore, the equation

v =fλ

becomes

c = fλ!

Solving an EM problem (cont)

• Problem: The wavelength of yellow light is 556 nm. What is the frequency?

• Answer: c = fλ

3.0 x 108 m/s = f(556 nm)

5.4 x 1014 Hz