Waves Unit 4: Pages 334 to 421 Chapter 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!)

NOTE Light may or may not behave as a wave – it is not seen but it is the main theory… we will discuss further!!!

Bobblehead aves/u10l0a.cfmhttp:// aves/u10l0a.cfm Tuning Fork

What is a wave? Wave: a disturbance that transfers energy through a medium vibration as their source.Whether ocean waves, waves on a string, earthquake waves, or sound waves in air, they all have a 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.

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? pdnr50&feature=relatedhttp:// pdnr50&feature=related eriesPlayList&v=XoYBAsHHXsk&list=PLF F513AD10F64B864http:// eriesPlayList&v=XoYBAsHHXsk&list=PLF F513AD10F64B864 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. NOTE: Particles can also transfer energy (we will discuss further later…)

Key Terms for Waves Rest Position Phase Difference Natural Frequency Resonance

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. Transverse 2. 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. Example: S waves (earthquakes)

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

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 westward c. north to south only d. 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 points that are moving in phase. Think of a wavelength as the distance between two humps. Symbol = λ (lamda) Unit = metre (m)

Key Terms for Waves Frequency - 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

Key Terms for Waves Period - time taken to produce one complete wave. Symbol = T Units = seconds (s) Formula: where t is time NOTE: DO NOT GET CONFUSED WITH WAVELENGTH AND PERIOD – MATH 11 IS NOT PHYSICS 11!

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. Phase - a description of a stage that a periodic motion has reached, usually by comparison with another such motion of the same frequency. Two varying quantities are said to be in phase if their maximum and minimum values occur at the same instant.

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

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

Example 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 = Hz = ~0.40 Hz period = 58 seconds/23 cycles = 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: seconds GIVEN: f = 440 Hz Find T T = 1 / f = 1 / (440 HZ) = s

The Wave Equation The 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 = λfv = λf But f = 1/T so… v = λ/T Velocity of electromagnetic waves is 3.0x10 8 m/s

Wave Speed Example 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) = 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.

Resonance Examples Bay of Fundy Tides When a choir sings Shattering of glass ( ) Allows us to pick up TV/radio signals (electrical resonance) MRIs – Magnetic Resonance Imaging (magnetic field allows doctors to look inside you!) 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. out-of-pha.htmlhttp://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?

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?