Waves Guided Notes Packet 1 Name:___________________

Oscillatory Motion

______________________ means to go back and forward

______________________ motion is very common

_________________________ _________________________ _________________________

_____________________________________– position where an object would rest if not disturbed.

__________________________________ x, θ – displacement from equilibrium position.

_________________________________ A, θ0 – the maximum displacement of an oscillating object from equilibrium.

__________________________________ – one complete oscillation

_________________________________(T) – the time it takes an oscillating system to make one complete oscillation.

_________________________________ (f) – the number of complete oscillations made by the system in one second.

Frequency = 1/period

units: 1/s = s-1 = 1 Hz (hertz)

Turn & Talk

What is the equilibrium position for a pendulum?

What is the difference between displacement and amplitude?

What is period? How do you find it?

Simple Harmonic Motion

Do Now

Explain why a pendulum oscillates using words and pictures.

Vocab Review!

What does the word oscillation mean?

When is oscillatory motion is called periodic motion?

We refer to these repeating units of periodic motion as __________________.

The time it takes to complete one cycle is called the _____________________.

Example: Earth’s rotation has a period of 24 hours, or 86,400 s

Simple Harmonic Motion

Pendulums and springs are special examples of motion that not only oscillatory and periodic, but also ______________.

Simple harmonic motion is a type of periodic motion in which the ____________________________________________ __________________________________________________________________________________________________

e.g. greater displacement = greater force

Restoring Force – CFUs

In which position(s) is the restoring force of the pendulum …

… greatest?

… zero?

… angled downward and towards the right?

In which position(s) is the restoring force of the sp

… greatest?

… zero?

… directed upwards

Springs can also be compressed!

Any _______________ (stretchable) material will act somewhat like a spring.

Calculating Net (Restoring) Force

In pendulums … In springs …

Look at the diagram. Fspring = kx

What forces cancel out? Where k = spring constant

x = displacement

What is the net force?

A B C D E F G

We Do: Calculating Net (Restoring) Force

An engineer measured the force required to compress a spring.

1) Based on the data, what is the spring constant?

2) Predict the force required to compress the spring by 3.5 mm.

Turn and Talk

1) If you stretch and release a slinky, you will notice that the amplitude of its motion decreases over time (why?). How does this decrease in amplitude affect the period of motion?

2) Will a grandfather clock run slower or faster if placed on the moon? Why?

3) How does doubling the mass affect the period of a pendulum? How does doubling the mass affect the period of a spring

Note: Amplitude ______________ affect period in pendulums or springs!

Force (N) Displacement (mm)

2 1.0

3 1.5

4 2.0

5 2.5

6 3.0

Conservation of Energy

Ideally, pendulums and springs both conserve energy. (Realistically, they lose energy over time due to __________________________).

In both cases, PE is maximum at _____________________________.

PE gradually converts to KE, and reaches zero at the equilibrium point.

KE shows the opposite trend – it is maximum at equilibrium and reaches zero at maximum displacement.

We have a simple formula for the PE in a spring.

You Do Problems

1) A spring stretches by 18 cm when a bag of potatoes weighing 56 N is suspended from its end.

a) Determine the spring constant, k

b) How much EPE does the spring have when it is stretched this far?

2) A pendulum swings from its release point, past equilibrium, to its highest point on the opposite side in 0.4 seconds. The highest point is 8 degrees above equilibrium. What is its frequency? Its period? Its amplitude?

PEspring =

3) You need to know the height of a tower but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower?

4) Billie releases the bob of his pendulum at an angle of 10° from the vertical. At the same time, Bobby releases the bob of his pendulum at an angle of 20° from the vertical. The two pendulums have the same length. Does Billie’s bob reach the vertical position before, after, or at the same time as Bobby’s bob? Explain.

Damping and Resonance

Damping is the ______________________________ of a wave.

All real pendulums and springs have damping.

• ________________________________________________________________

• Amplitude of motion becomes smaller, until it ceases

Some systems are designed to heavily damped, such as

shock absorbers on a car

Damping mechanisms in the foundations of buildings in earthquake zones

Resonance is ____________________________________________ of oscillation of a system that occurs when an ______________________________________________________________________________________________ – the frequency it would naturally oscillate at if hit once.

Examples:

Pushing a child on a swing Shattering a kidney stone with ultrasound

Vibration of the strings that differ by one or more octaves (and to a lesser extent, other harmonic intervals) when a note is played on a stringed instrument.

Shattering glass with your voice Tacoma-Narrows Bridge

Wave Characteristics

What is a wave?

Watch the two waves.

How do the particles move?

Key point: Waves carry ________________ not _____________.

Definition: A wave is a disturbance that _______________________________ through matter or space ____________________________________________________ .

The energy carried by a wave can be substantial – think of earthquakes, tsunamis, or the heat and light of the sun.

Transverse Waves

The particles of the medium oscillate __________________________to the direction of energy transfer/propagation of the wave.

Examples:• earthquake secondary waves, • waves on a stringed musical instrument• waves on the rope, • EM waves: light, radio waves, microwaves…

Longitudinal Waves

The particles of the medium oscillate __________________________ to the direction of energy transfer/propagation of the wave.

Creates areas of increased and decreased density• Areas of high density / pressure = _____________________• Areas of low density / pressure = _____________________

Examples• Sound waves• Earthquake p waves• Compression in a spring

Wave Characteristics

Wavelength (λ) The ________________________________________________________ of a wave measured in meters

Phase Two points on a wave that occur in the same position within the wave cycle – that is, they are one or more

whole wavelengths apart -- are said to in phase. Points in a wave medium can be anywhere from 0° to 360° out of phase with each other. A trough and a crest are 180° out of phase with each other.

Amplitude, A

● the ______________________________________________________________________________________. ● measured in m ● the _________________________________________, the ____________________________________of the wave ● if a wave doesn’t lose energy, then its amplitude remains constant; if the wave does lose energy then the amplitude decreases over time (damping)

Period, T

● is the _____________________________________________________________________________________. ● measured in seconds

Frequency, f

● is the _______________________________________________________________________________________. ● measured in cycles per seconds or Hz

Wave speed, v

● The _______________________________________________________________________________. ● ___________________________________________________________ through which a wave travels!

Waves travel faster through material that is stiffer and through material that is less dense.

Speed of sound in: air: 343 m/s helium: 1005 m/s water: 1500 m/s bone: 3000 m/s steel rod: 5000 m/s glass: 4500 m/s

Mechanical vs. EM waves

Mechanical Waves

● _________________________________________________________________________________ ● Make the particles of the medium oscillate at frequency of the wave Examples: waves on a string, sound waves, earthquakes, etc.,

EM (electromagnetic) waves

● __________________________________________________________________________________ ● Do not cause the particles of the medium to oscillate ● Made up of changing electric and magnetic fields ● always occur as transverse waves ● In a vacuum, EM waves travel at the speed of light c ≈ 3 x 108 m/s (EM waves travel more slowly through a medium)

Wave Equation

A wave generator was used to generate waves of different frequencies in a rope. Two different tensions of rope where used. The wave speed and wavelength were measured.

Use the data in the table to answer the following questions

a) Which variable(s) affected wave speed?

b) How are wavelength, frequency, and speed related?

Check Your Understanding

You Do

1. A sound wave produced by a clock chime is heard 515 m away 1.5 s later.

(a) What is the speed of sound in the air there?

(b) The sound wave has a frequency of 436 Hz. What is the period of the wave?

(c) What is the wave's wavelength?

2. A hiker shouts toward a vertical cliff 465 m away. The echo is heard 2.75 s later.

(a) What is the speed of sound in air there?

(b) The wavelength of the sound is 0.75 m. What is the frequency of the wave?

(c) What is its period?

Sound Guided NotesDefine the following terms, giving units and variables for 5-8.

1. Wave ____________________________________________________________________________________ __________________________________________________________________________________________

2. Longitudinal wave ___________________________________________________________________________ __________________________________________________________________________________________

3. Transverse wave ___________________________________________________________________________ __________________________________________________________________________________________

4. Mechanical wave ___________________________________________________________________________ __________________________________________________________________________________________

5. Frequency _________________________________________________________________________________ __________________________________________________________________________________________

6. Wavelength ________________________________________________________________________________ __________________________________________________________________________________________

7. Pitch _____________________________________________________________________________________ __________________________________________________________________________________________

8. Amplitude _________________________________________________________________________________ __________________________________________________________________________________________

The nature of soundWhat kind of waves are sound?

___________________ - caused by oscillations of atoms ____________________ - creates areas of high and low pressure

What are areas of high pressure called?

What are areas of low pressure called?

Frequency of Sound

• The frequency of sound refers to the ___________________________________________ made by atoms, and it is measured in ______________ (s-1).

• Frequency = ________________

• Human ear can hear between 20 – 20 000 Hz.

• _________________ – below 20 Hz

• _________________ – above 20 000 Hz

• Bats and dolphins use ultrasound for navigation; elephants and whales communicate over large distances using infrasound.

Loudness of Sound

Which variable do you think corresponds to the loudness of sounds? ________________________________

Loudness is measured on a decibel scale

Speed of Sound

Speed of sound depends on …

________________________________________________________.

________________________________________ (though high frequency

waves will have short wavelengths and low frequency waves will have

high wavelengths in accordance with λf = v )

Sound is typically fastest in solids, then in liquids, and slowest in gases.

Sound is faster in warm, humid air than in cold, dry air.

Doppler Effect

The _____________________________________________________ that occurs when the _____________________

________________________________________________________________________________________________.

General Rule:

If the source and the observer are moving

… closer together the perceived frequency is ______________

... farther apart the perceived frequency is ________________

Represents a stationary sound source

The distance between wave fronts is the wavelength.

All observers will hear the _______________

Represents a source moving at v

Wave fronts are still produced with the same frequency but are bunching up in the direction of travel

Observer in front of the source hears a _________________ sound

Observer behind the source hears a ____________________, lower frequency sound.

This is called a ______________________________.

Doppler Effect Applications

Doppler shift can be used to determine the relative speed of objects. Waves are directed at an object, they reflect (bounce back) and are picked up by a receiver. The ____________________________________________________ ___________________________________________________.

Examples:

ultrasound waves to show blood velocity

microwaves in radar guns

The light from distant stars often appears to be ‘------------------------------------- indicating that those galaxies are --____________________________________.