Waves

Unit 4: Pages 334 to 421Chapter 8 in text

What do you already know?

• What is a wave?• Where do we “see” waves in our everyday

lives?• Why are waves important to physicists?

Waves - Everyday• Earthquakes• Tsunamis• Sound waves• Radio waves• Light waves***• Regular ocean waves• Springs (Slinky!)• car suspension

NOTE

• Light may or may not behave as a wave –it is the main theory… most physicists believe light behaves as a wave of electromagnetic radiation

• Some physicists believe light is made of massless particles called photons not waves.

Bobblehead

• http://www.physicsclassroom.com/class/waves/u10l0a.cfm

• Bobblehead description:– The head moves back and forth but this does

not go on forever.– Why does it start?– Why does it stop?

Tuning Fork

What is a wave?• Wave: a disturbance that transfers energy

through a medium

• Whether ocean waves, waves on a string, earthquake waves, or sound waves in air, they all have a vibration as their source.vibration as their source.

• Waves move large distances across the surface of a lake or the sea, yet the water itself does not travel those distances. Only the ENERGY!

Question

• Minute after minute, hour after hour, day after day, ocean waves continue to splash onto the shore. Explain why the beach is not completely submerged and why the middle of the ocean has not yet been depleted of its water supply.

Answer

• Ocean waves do not transport water. An ocean wave could not bring a single drop of water from the middle of the ocean to shore. Ocean waves can only bring energy to the shore; the particles of the medium (water) simply oscillate about their fixed position. As such, water does not pile up on the beach.

TRUE or FALSE: • In order for John to hear Jill, air molecules

must move from the lips of Jill to the ears of John.

FALSE!

• A sound wave involves the movement of energy from one location to another, not the movement of material. The air molecules are the particles of the medium, and they are only temporarily displaced, always returning to their original position.

Why are waves important to physicists?

• http://www.youtube.com/watch?v=TGaM8pdnr50&feature=related

• http://www.youtube.com/watch?feature=SeriesPlayList&v=XoYBAsHHXsk&list=PLFF513AD10F64B864

• Waves are very important in engineering (buildings, bridges), seismology, etc. Waves explain how ENERGY MOVES.

How does this relate to the physics we did already???

• Waves transfer ENERGY. However, there must be a medium for the energy to move through (ie, matter must be around even though the medium does not move itself)

• NOTE: Particles can also transfer energy (we will discuss further later…)

What is a vibration?• Vibration: the motion of an object that regularly

repeats itself, back and forth, over the same path.

• Other words for vibration: oscillation, cycle

• Periodic Motion: when an object moves in a repeated pattern over regular time intervals.

• YOU HAVE LOOKED AT VIBRATIONS IN MATH 11/11 AD.

Types of Waves

• There are two types of waves.1. Transverse2. Longitudinal

Transverse Waves…Transverse waves are when the displacement is perpendicular to the direction of the wave…

Transverse waves are the ones most people can draw.

Example. Water ripples on the surface of the pond, S waves (earthquakes), radiowaves, x-rays, and light waves (all electromagnetic waves) x-rays

http://www.kettering.edu/physics/drussell/Demos/waves/wavemotion.htmlhttp://www.youtube.com/watch?v=UHcse1jJAto

Longitudinal Waves…Longitudinal waves are when the displacement is parallel to the direction of the wave…

Example: Sound waves, ultrasound waves

http://www.youtube.com/watch?v=Rbuhdo0AZDU

http://www.gcse.com/waves/waves2.htm

Slinkys• When using a slinky, move your hand from side to side

some humps move away from you along the slinky. Although the waves move along the slinky, the movement of the slinky is side to side. This is a transverse wave. The particles carrying the wave in the slinky move at right angles to the direction of wave motion.

• You produce a different wave when you move your hand backwards and forwards along the slinky. This sort of wave is a longitudinal wave. The particles carrying the wave in the slinky move backwards and forwards along the direction of wave motion.

Questions for you!

• 1. A transverse wave is transporting energy from east to west. The particles of the medium will move_____.

a. east to west only b. both eastward and westwardc. north to south onlyd. both northward and southward

• Answer: D• The particles would be moving back and

forth in a direction perpendicular to energy transport. The waves are moving westward, so the particles move northward and southward.

• 2. A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a ____.

• A. Longitudinal• B. Transverse

• LONGITUDINAL!

• 3. Describe how the fans in a stadium must move in order to produce a longitudinal stadium wave. How would they make a transverse wave?

• The fans will need to sway side to side. Thus, as the wave travels around the stadium they would be moving parallel to its direction of motion. If they rise up and sit down, then they would be creating a transverse wave.

• 4. A science fiction film depicts inhabitants of one spaceship (in outer space) hearing the sound of a nearby spaceship as it zooms past at high speeds. Critique the physics of this film.

• This is an example of faulty physics in film. Sound is a wave and could never be transmitted through the vacuum of outer space (no medium!)

How are waves produced?

• Waves are produced by a wave pulse.

• A wave pulse is a single disturbance that travels through a medium (water, air, glass, etc..)

• A traveling wave is a series of wave pulses at regular intervals.

Key Terms for Waves

Wavelength - the shortest distance between two repeated points in a wave. Think of a wavelength as the distance between two humps.

Symbol = λ (lamda)Unit = metre (m)

Key Terms for WavesFrequency - the number of complete waves produced per

second.

Symbol = f Units = Hertz (Hz) 1 Hz = 1/s

(Named after Henry Hertz who discovered radio waves)

Formula: where N is number of cycles, t is time

Formula where T is the period

Tf 1

tNf

Key Terms for Waves

Period - time taken to produce one complete wave.

Symbol = TUnits = seconds (s)

Formula: where t is time

NOTE: DO NOT GET CONFUSED WITH WAVELENGTH AND PERIOD – MATH 11 IS NOT PHYSICS 11!

NtT

Key Terms for Waves

• Amplitude - the greatest displacement of the wave away

from its undisturbed position. Think of the amplitude as the height of a hump.

Key Terms for Waves• Rest Position: When a pendulum or a mass on

a spring is not in motion but is allowed to hang freely, the position it assumes is called its rest position. (also called equilibrium position from Hooke’s Law and sinusoidal axis in math 11)

• Trough: lowest point on a wave (local min in math 11)

• Crest: highest point on a wave (local max in math 11)

Questions for you!Consider the diagram below in order to answer

questions #1-2.

• 1. The wavelength of the wave in the diagram above is given by letter ______.

 • 2. The amplitude of the wave in the diagram above is

given by letter _____. 

• 1. A• 2. D

3. Indicate the interval that represents one full wavelength.

• a. A to C • b. B to D• c. A to G• d. C to G

• 3. D

Examples

• 1) A mass suspended from the end of a spring vibrates up and down 24 times in 36 seconds.

• A) What is the frequency of the vibration?• B) What is the period of the vibration?

Answer

• A) F = N/t• F = 24/36 = 0.67 Hz

• B) T = t/N • T = 36/24 = 1.5s

Example 2

• A pendulum is observed to complete 23 full cycles in 58 seconds. Determine the period and the frequency of the pendulum.

Answer

• frequency = 23 cycles/58 seconds = 0.39655 Hz = ~0.40 Hz

• period = 58 seconds/23 cycles = 2.5217 sec = ~2.5 s

Example 3

• A mass is tied to a spring and begins vibrating periodically. The distance between its highest and its lowest position is 38 cm. What is the amplitude of the vibrations?

Answer

• Answer: 19 cm

Questions…

• Page 341, questions 1 to 4

Quick Review…

• The period of the sound wave produced by a 440 Hertz tuning fork is ___________.

• Answer: 0.00227 secondsGIVEN: f = 440 HzFind TT = 1 / f = 1 / (440 HZ) = 0.00227 s

The Wave EquationThe wave equation relates the speed of the wave to its frequency and wavelength:

Wave speed (v) = frequency (f) x wavelength () in m/s in Hz in m

V

f

Wave Equation• Wave velocity - the velocity at which wave crests

(or any other part of the wave) move.• v = v = λλff

• But f = 1/T so…

• v = λ/T

• Velocity of electromagnetic waves is 3.0x108 m/s

Wave Speed Example 1

• A spring vibrates at 2.8 Hz. This produces a wave with wavelength 36cm. Calculate the speed of the wave.

• Answer: v = fλ• v = (2.8)(0.36)

= 1.008 m/s = 1.0m/s

Example 2

• Water waves with wavelength 1.8m produced in a wave tank travel with a speed of 2.50 m/s. What is the frequency of the vibrations that produced them?

• Answer: v = fλ f = v/ λ f = 2.50/1.8 f = 1.4 Hz

Try These

• Page 349, questions 5, 6• Page 350, questions 7, 8a/b, 9

Natural Frequency

• A pendulum or spring (wave) has a natural frequency – the speed at which it vibrates freely.

• The frequency depends on the length of the spring, etc. Shorter springs and pendulums have higher natural frequencies than longer ones.

• Example: Guitar Strings – the higher strings are shorter (harder to hold!!!)

Resonance• Phenomena that occurs when energy is added

to a vibrating system at the same frequency as its natural frequency.

• Resonance makes the amplitude of the vibrations become larger.

• Example: When you push someone on a swing (at the natural frequency) they will go higher! This is because energy is added. The vibrations and your push are IN PHASE.

In Phase

• In Phase - Two varying quantities are said to be in phase if their maximum and minimum values occur at the same instant. The two periodic motions must have the same frequency for this to occur.

Resonance Examples• Bay of Fundy Tides• When a choir sings• Shattering of glass (

http://www.youtube.com/watch?v=17tqXgvCN0E )• http://www.youtube.com/watch?v=WFbUpUE9KiU&feature=related

• Allows us to pick up TV/radio signals (electrical resonance)• MRIs – Magnetic Resonance Imaging (magnetic field allows doctors

to look inside you!)• http://www.youtube.com/watch?v=H0adTNhzGxU

• Your car going at a certain speed starts to vibrate! (poor wheel alignment)

• Tacoma Narrows Bridge (video from before!) – wind was IN PHASE with natural frequency of bridge

Out of Phase

• When two pendulums are moving in unison, they are said to be IN PHASE.

• When they move in opposite directions they are said to be OUT OF PHASE.

• http://boingboing.net/2011/05/13/beautiful-out-of-pha.html

In Phase/Out of Phase Example• If I dropped two rocks in water and they

produced the same waves, there are some places where the waves arrive in phase. This means that two crests arrive at the same time. The two crests move the water upwards to make a larger wave.

• In other places, the waves will arrive out of phase. When a crest arrives from one rock, a trough arrives from the other rock. This time, the effect of the waves cancel each other out. The water does not move at all.

Questions for You!

Page 343, questions 1, 2, 3, 4, 6, 7

Why would we need to know the speed of a wave anyway???

• To predict when a tsunami will strike the shore.

• To determine the epicentre of an earthquake. To do this, seismologists look at the difference in time it takes for a P-wave to reach a location and an S-wave to reach a location.

Reading Seismographs

• Which city is farthest from the earthquake?

• Which city is closest to the earthquake?

• How do you know?

Try This

• Get a cup of water• Get a few different tuning forks• Strike the tuning fork. You can’t see the

air move.• Put the vibrating tuning fork in the water.

What happens?

• Get 2 cups• Attach a string• What happens if you talk in one cup?• Explain why the other person can hear!

How does a record work?

• http://www.videojug.com/interview/fun-science-demonstrations

• 2nd section

Wave Interference• The speed of a wave does not depend on the

amplitude or frequency. It depends on the properties of the medium in which it travels.

• Although a wave with a larger amplitude transfers more energy, it moves with the same speed as a smaller amplitude wave through a given medium.

• As long as the material is the same, the speed of high and low frequency waves is the same.

What influences the size of a wave?

• What influences the speed of a wave?

Key Terms for Waves

• Rest Position (equilibrium)• Phase Difference• Natural Frequency• Resonance