1. Waves
Chapter 25

2. Waves
Waves are everywhere. Sound waves, light waves, water waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of waves.
Waves are an energy transport phenomenon, a way to transport energy from one location to another.
Waves are a disturbance that travels through a medium from one location to another; a wiggle in space and time.
The medium is a substance or material that carries the wave.
Waves are caused by vibrations
A vibration (or oscillation) is a back-and-forth or up-and-down motion; a wiggle in time.

3. Types of Waves
We will discuss two types of waves longitudinal (or compression) and transverse
Transverse wave - oscillations are transverse (perpendicular) to the direction of motion
Longitudinal (or Compression) wave - oscillations are in the direction of motion or parallel to the direction of motion.

4. Anatomy of a Wave
The parts of a wave include crest, trough, wavelength, amplitude, frequency and period
crest
trough
The points A and F are called the CRESTS of the wave.
The points D and I are called the TROUGHS of the wave.
This is the point where the wave exhibits the maximum amount of positive or upwards displacement
These are the points where the wave exhibits its maximum negative or downward displacement.

5. Anatomy of a Wave
The distance between the dashed line and point A is called the amplitude of the wave.
The amplitude is the maximum displacement that the wave moves away from its equilibrium.
The distance between two consecutive similar points (in this case two crests) is called the wavelength.
The wavelength is also the length of the wave pulse.
Wavelength
Wavelength
Amplitude
Wavelength

6. Wave Frequency and Period
Frequency (f) measure how often something happens over a certain amount of time (# of waves/second)
We can measure how many times a pulse passes a fixed point over a given amount of time, and this will give us the frequency.
The period (T) is the time it takes for one cycle (wave) to complete.
The period is also is the reciprocal of the frequency.
T = 1 / f
f = 1 / T

7. The Period of a Pendulum
The motion of a pendulum and the motion of a mass on a spring can be described using a wave.
The period of a pendulum is the time is takes for one full back and forth motion.

8. Wave Speed (or velocity)
Wave speed is the distance the disturbance travels in a fixed amount of time.
Wave speed, s, or wave velocity, v, can be determined from the distance a wave pulse travels divided by the time that the pulse takes to travel that distance.
s = d/t or v , where d is the distance the wave pulse traveled and t is the time is took to travel that distance.

9. Speed Speed is a measure of how fast something is moving.
It is the rate at which a distance is covered
Units of speed could be: km/h, m/s, mi/h, ft/s
We will use units of m/s for speed.
The formula relating speed, distance and time is s = d/t s d t

10. Using the triangle to solve problems
Cover up the letter you wish to calculate, then look at how the letters left are arranged.
Are they next to each other? Then multiply
Are the arranged so that one is over another? Divide
Try it. Find the equation for distance, and time using the triangle.
d = s x t
t = d/s s d t

11. Problem Solving Tips
1. Read the problem , and try to restate it in your own words. It generally is helpful to make a sketch. Write down any key words or concepts that come to mind. 2. Make a list of the physical quantities that are given as initial conditions, and assign the symbols that are used in the text to each of them. 3. Make a list of the physical quantities that you are being asked to determine and assign symbols to them as well. 4. Try to identify what physical principle is involved, and the law or equations that connect the given quantities and those you want to determine. More than one step may be required. If the connection is unclear, a dimensional analysis may help. For clues, examine the solutions to sample problems in the text, student solutions manual and web site. 5. Once the method of solution is identified, be careful about units and significant figures when calculating. Show all steps involved, since some credit is allowed for partial solutions. Be sure to indicate the units when the answer is a physical quantity or parameter. Double-check your work. 6. Problems have been selected for homework, quizzes and tests may vary considerably and randomly in difficulty, so if you are stuck on one, go on to the next and come back to it. Solving another problem will give you confidence and perhaps even a clue. 7. Remember that learning to do physics is like learning to play a sport or a musical instrument. You will only get better with practice, practice, practice. Solving physics problems is not a waste of your time! The methodology outlined above for problem solving will often be adaptable to situations or problems that you will encounter later in your profession. The practice that you get now will hone your analytical and problem-solving skills, and make you more valuable to your organization.

12. Speed Questions
1) During the first hour of a trip, a person travels 50 km. During the second hour, the person travels an additional 100 km. During the third hour, the person travels an additional 150 km.
What is the person’s average speed for the entire trip?
Moving at the average speed, how far would the person travel in 5 hours?
2) If the distance between London and NY is 3600 miles, how long would it take the Concorde flying at 1200 miles/hr to reach London from NY?
3) How fast is a car traveling if it travels 13 m in 0.5 s?
4) Challenge: How long does it take light, which travels at 300,000,000 m/s to pass through a sheet of 3 mm glass?

13. Velocity and Speed
In physics we distinguish between speed and velocity:
Speed refers to how quickly an object moves.
Velocity can be defined as speed in a given direction.
Speed and velocity triangles are similar because the equation relating velocity is v = d/t. v d t

14. Wave Speed (or velocity)
Wave speed can be determined from the distance the disturbance travels in a fixed amount of time.
Wave speed can also be determined from the product of the wavelength and the frequency
velocity = wavelength x frequency
v = f
This equation is known as the wave equation

15. Wave Questions
Rhonda sends a pulse along a rope. How does the position of a point on the rope, before the pulse comes, compare to the position after the pulse has passed?
Why don't incoming ocean waves bring more water on to the shore until the beach is completely submerged?
In order for a medium to be able to support a wave, the particles in the wave must be
a) frictionless.
b) isolated from one another.
c) able to interact.
d) very light.
A transverse wave is transporting energy from east to west. How will the particles of the medium will move?
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 _______________.

16. More Wave Questions
6) In the diagram above, the wavelength is given by what letter? 7) In the diagram above, the amplitude is given by what letter? 8) A wave has an amplitude of 2 cm and a frequency of 12 Hz, and the distance from a crest to the nearest trough is measured to be 5 cm. Determine the period of such a wave. 9) A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is ________. 10) A pendulum makes 40 vibrations in 20 seconds. Calculate its period? 11) Mac and Tosh are resting on top of the water near the end of the pool when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave. 12) A marine weather station reports waves along the shore that are 2 meters high, 8 meters long, and reach the station 8 seconds apart. Determine the frequency and the speed of these waves.

17. Wave Behavior
Now the we know the parts of a wave and how we describe and analyze them, we can look at wave behavior
In the next section we will look at interference, the boundary behavior of waves, standing waves and the Doppler Effect.
The Doppler Effect

18. The Doppler Effect
The Doppler Effect is the apparent change in frequency of a wave due to relative motion between source and observer.
As the sound move toward the observer, the apparent frequency increases, the waves get compressed.
As the sound moves away from the observer, the apparent frequency decreases, the waves get “stretched out”
A sound wave frequency change is noticed as a change in pitch.

19. Doppler Shift for Light

20. Doppler and Line of Sight
We are only
sensitive
to motion
between
source and
observer
ALONG
the line of
sight.

21. Interference and the Superposition Principle
Suppose two waves pass through the same medium. What happens?
Wave interference is the phenomenon which occurs when two or more waves meet while traveling along the same medium.
The superposition principle tells us how waves interact.
The principle of superposition is sometimes stated as follows: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
Algebraic sum of two waves

22. Constructive Interference
Constructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction. The resulting displacement is greater than the displacement of the two interfering pulses alone.

23. Wave Addition

24. Destructive Interference
Destructive interference is a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. The resulting displacement is less than the displacement of the two interfering pulses alone.

25. Wave Subtraction

26. Two Opposite Waves
When the two opposite waves arrive at the same location, they cancel, destructively.

27. Interference Water waves from two oscillating sources
Computer Simulation
Ripple Tank

28. Boundary Behavior of Waves
The behavior of a wave when it reaches the end of its medium is called the wave’s boundary behavior.
When one medium ends and another begins, that is called a boundary.
One type of boundary that a wave may encounter is that it may be attached to a fixed end.
The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse.

29. Change in Medium
In this situation part of the wave is reflected, and part of the wave is transmitted.
The transmitted pulse is upright, while the reflected pulse is inverted.
The speed and wavelength of the reflected wave remain the same, but the amplitude decreases.
The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse.

30. Standing Waves
When a reflected wave interferes with an incident wave, a standing wave can form.
Nodes are points of no motion
Anti-nodes are points of maximum motion

31. Harmonics
There are a variety of patterns by which the guitar string could naturally vibrate; each pattern is associated with one of the natural frequencies of the guitar strings.

32. Sources Conceptual Physics by Paul Hewitt www.physicsclassroom.com
pls.atu.edu/physci/physics/people/robertson/courses/phsc1013/PHSC1013-Waves.ppt –
Waves and Vibrations -Physics: Mr. Maloney