12-3 properties of waves1. Distinguish local particle vibrations from overall wave

motion.2. Differentiate between pulse waves and periodic waves.3. Interpret waveforms of transverse and longitudinal waves4. Apply the relationship among wave speed, frequency, and

wavelength to solve problems.5. Relate energy and amplitude.

What is a wave?• A WAVE is the motion of disturbance. Some

disturbance can only go through a medium, others can go through both a medium or vacuum (empty space).

• A MEDIUM is a body of matter, such as water, air, people, slinky, etc.

• All waves are produced by a vibrating SOURCE.

– Sound wave is produced by a vibrating vocal cord.

– Radio waves is produced by accelerating electrons in a transmitter.

Waves and energy transfer• Wave can transfer ENERGY from one place to

another – Either through vibrations of particles in a medium,– Or by repeated small changes in the strength of a

field.• The source provides the initial vibrations, but there is

NO ACTUAL TRANSFER OF MASS from the source.• ONLY ENERGY is transferred from the source.

Mechanical waves vs. electromagnetic waves

• An ELECTROMAGNETIC WAVE is a wave capable of transmitting its energy through a VACUUM (i.e., empty space). Electromagnetic Wave can transfer ENERGY from one place to another by repeated small changes in the strength of a field. A RADIO wave is an example of electromagnetic wave.

• A MECHANICAL WAVE is a wave NOT capable of transmitting its energy through a vacuum. Mechanical waves REQUIRE A MEDIUM in order to transport their energy from one location to another. A SOUND wave is an example of a mechanical wave. Sound waves are incapable of traveling through a vacuum.

Pulses and Periodic Waves• A wave may be classified as either a pulse or a periodic wave.• A PULSE is a SINGLE vibratory disturbance that transfers energy

but NOT mass.

• A WAVE is a PERIODIC vibratory disturbance that transfers energy but NOT mass.

What is the direction of motion in the medium?

v v

As the wave travels to right or left, a single point in the medium will only moves UP or DOWN, IN THE SAME DIRECTION AS THE POINT BEFORE IT.

Example #1

• As shown in the diagram, a pulse is moving along a rope. In which direction will segment X move as the wave passes through it?

a. down, only b. up, only c. down, then up d. up, then down

• The diagram shows a pulse moving in the direction shown by velocity vector v.  At the instant shown, a cork at point P on the water's surface is moving toward

a. A b. B c. C d. D

Example #2

1. In the next instant of time, indicate

a. The direction of motion of point A.

b. The direction of motion of point B.

c. The direction of motion of point C.

d. The direction of motion of point D.

vClass work – today’s date

2. The diagram below represents a transverse wave traveling to the right through a medium. Point A represents a particle of the medium. In which direction will particle A move in the next instant of time?

3. Which of the following is transmitted by a pulse? a. energy and mass b. mass only c. energy only

4. The energy contained in a pulse is related to its: (1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only

5. As pulses travel they lose: (1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only

Transverse Wave – particles of the medium move PERPENDICULAR to the wave’s direction of travel

Transverse waves vs. Longitudinal waves

Longitudinal Wave – particles of the medium move PARALLEL to the wave’s direction of travel.

Transverse Wave – particles of the medium move PERPENDICULAR to the wave’s direction of travel

Motion of particles in the medium

v crest

trough

wavelength (λ)

A

amplitude

transverse waveCrest, trough, A, λ, T, f

• CREST: the highest point in a waveform.• TROUGH: the lowest point in a waveform• AMPLITUDE (A): maximum displacement of a particle on the

medium from its rest (equilibrium) position. From rest to crest or from the rest to trough. The amount of ENERGY carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by a high amplitude; a low energy wave is characterized by a low amplitude.

• WAVELENGTH (λ): length (distance) of one complete wave cycle. It can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave

• PERIOD (T): time of once complete wave cycle. It is measured in unit of time (sec, min, hr…)

• FREQUENCY (f): number of cycles per unit of time. (1/T)

Longitudinal Wave – particles of the medium move PARALLEL to the wave’s direction of travel.

rarefaction

compression

Motion of particles in the medium

vwavelength (λ)

SOUND WAVESFaster in DENSE mediums

Longitudinal waveCompression, Rarefaction, A, λ, T, f

• COMPRESSION: the most compressed part in a waveform.• RAREFACTION: the most stretched part in a waveform• AMPLITUDE (A): how much the particles are stretched or

compressed. The amount of energy carried by a wave is directly related to the amplitude of the wave.

• WAVELENGTH (λ): the distance from one compression to the next compression, or from one rarefaction to the next rarefaction.

• PERIOD (T): the time from one compression to the next compression, or from one rarefaction to the next rarefaction.

• FREQUENCY (f): number of cycles per unit of time. (1/T)

Frequency and speed• The quantity frequency is not speed. • The wave speed refers to HOW FAST the wave is

moving (m/s). • The wave frequency refers to HOW OFTEN the

medium vibrates up and down. (# of cycles/second or Hz).

• A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities.

Examples of Longitudinal and transverse wave

• Transverse: – Wave on a string– Stadium wave– Wave on a slinky– ELECTROMAGNETIC WAVES (light, RADIO, microwaves, UV

rays, etc)

• Longitudinal: – SOUND WAVE– Wave on slinky– Earthquake

http://www.suu.edu/faculty/colberg/Hazards/Earthquakes/31_surface_waves_earthquakes/31.html

• Find the amplitude and wavelength of waves A, B, C.

Example #1

Example #2• A longitudinal wave moves to the right through a uniform

medium, as shown below. Points A, B, C, D, and E represent the positions of particles of the medium.

1. Describe the motion of the particle at position C.

2. Which two points represent the wavelength of this wave?

Wave VelocityWaves have a definite direction of travel.

• Wave period (T) = TIME FOR ONE WAVE CYCLE

• Wavelength (λ)= DISTANCE FOR ONE WAVE CYCLE

Equation

fT

v

Variables Affecting Wave Speed

• The speed of a wave is not dependent upon properties of the wave itself (frequency, period, amplitude, wavelength). Rather, the speed of the wave is dependent upon the properties of the MEDIUM ONLY. Only an alteration in the properties of the medium will cause a change in the speed.

Example #1• What is the time required for the sound

waves (v = 340 m/s) to travel from the tuning fork to point A?

Example #2• A teacher attaches a slinky to the wall and

begins introducing pulses with different amplitudes. Which of the two pulses (A or B) below will travel from the hand to the wall in the least amount of time?

An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves that reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. The camera lens then focuses at that distance. Now that's a smart camera! If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, then how far away is the object?

Example #3

A wave with a frequency of 1.5 hertz is moving through a heavy spring where its wavelength is 2.0 meters.• What is the speed of this wave?• What wavelength would the wave have if it moved into a lighter

spring where its speed was 6.0 meters per second?

• What would probably happen to the amplitude of this wave after it moves into the lighter spring?

v = 3.0 m/s

λ = 4.0 m

Amplitude would increase

Example #4

summary• Wave speed is dependent upon medium properties• Even though the wave speed is calculated by

multiplying wavelength by frequency, an alteration in wavelength DOES NOT affect wave speed.

• Rather, an alteration in wavelength affects the frequency in an inverse manner. A doubling of the wavelength results in a halving of the frequency; yet the wave speed is not changed.

PHASE• Phase is the fraction of the wave cycle which has elapsed

relative to the origin. • Points on a periodic wave moving in the same direction and

having the same displacement from their rest position (same up or same down) are said to have the same phase, or to be “IN PHASE.”

• Points on a periodic wave having the opposite displacement from their rest position and are moving in the opposite direction are said to have be “OUT OF PHASE”

Points C & E are out of phase.

Points B & F are not in phase b/c B is going up, F is going down

Points A & E are in phase

• If two points are in phase, they could only be multiple of wavelength apart, such as 1λ (360o), 2λ (720o), 3λ(1080o), …

• If two points are out of phase, they could only be multiple of half wavelength apart, but not whole wavelength apart, such as ½ λ (180o), 1½ λ (540o), 2½ λ (900o),…

Points in phase:

A, C, & E

B, D

points are out of phase: A, BA, D B, CB, E

Example #1

• Points in phase:– A & F– D & I– C & H– B & G– E & J

• Points out of phase: – B & E, – E & G, – G & J, – B & J

Example #2

• Which point on the wave diagram is in phase with point A?

1. E 2. B 3. C 4. D

Class work – today’s date1. In the diagram, the distance between points A and B on a

wave is 5.0 meters. What is the wavelength of this wave?

2. The diagram represents waves A, B, C, and D traveling in the same medium. Which two waves have the same wavelength?

a. A and B b. A and C c. B and D d. C and D

3. The diagram below shows two points, A and B, on a wave train. How many wavelengths separate point A and point B?

4. Example: what is the frequency of the wave?

5. Determine the amplitude, frequency and period of the wave.

6. How are electromagnetic waves that are produced by oscillating charges and sound waves that are produced by oscillating tuning forks similar?

a. Both have the same frequency as their respective sources. b. Both require a matter medium for propagation. c. Both are longitudinal waves. d. Both are transverse waves.

7. The speed of a wave depends upon (i.e., is causally affected by) ...a. the properties of the medium through which the wave travels b. the wavelength of the wave.c. the frequency of the wave.d. both the wavelength and the frequency of the wave.

8. As the wavelength of a wave in a uniform medium increases, its speed will _____.a. decreaseb. increasec. remain the same

9. The diagram represents a wave traveling in a uniform medium. Which two points on the wave are in phase?

a. A and C b. A and E c. B and D d. B and F

10. The diagram shows a parked police car with a siren on top.  The siren is producing a sound with a frequency of 680 hertz, which travels first through point A and then through point B, as shown.  The speed of the sound is 340 meters per second.

• If the sound waves are in phase at points A and B, the distance between the points could be

a. 1λ b. ½ λ c. 3∕2 λ d. ¼ λ

11. What is the speed of a water wave with a wavelength of 10 meters if it has a frequency of 0.15 Hz?

12. A man on a beach notices that four waves arrive on the shore every 20 seconds. What is the frequency of the waves?

13. A sound wave travels from air to metal. What happens to its speed as it makes this change?

14. Why is the sound from a speaker louder when you sit closer to it?

15. What is speed of a wave with a frequency of 10 hertz if its wavelength is 3 meters?

16. What is the wavelength of a wave with a frequency of 6 hertz if it is moving at 30 meters per second?

17. What is the frequency of a wave that is moving at 15 meters per second if its wavelength is 7.5 meters? What is this wave’s period?

18. Mark each diagram or statement with a “T” if it describes a transverse wave or an “L” if it describes a longitudinal wave.

Particles in this type of wave move parallel to the direction of wave travel.

Particles in this type of wave move perpendicular to the direction of wave travel.

This wave moves more quickly in dense mediums than sparse ones.

This wave moves more quickly in sparse mediums than dense ones.

a.

b.

c.

19. What is the wavelength of each of the waves shown below?

20. What is the amplitude of each of the waves shown below?

a. b.

21.Pick a set of points that are: (a) in phase (b) 90° out of phase (c) 180° out of phase

22. Determine the direction in which each particle shown in the diagram will move in the next instant of time if the wave moves to the right.

23. In which type of wave will particles move north and south if the wave travels east to west? (1) longitudinal (3) circular

(2) transverse (4) torsional

24.How will particle A move in the wave shown below?