Waves

Homework

Read pages 381 – 386Answer Questions on

Page 386 # 16, 17, 18, 19, 20, 21

I. Vibrations and Waves

A. Vibrations1. back and forth motion (like a

pendulum) in time2. Period (T) - the amount of time

required for one complete cycle of a vibration

a. Measured in seconds

3. the vibratory motion of an object such as a pendulum or a mass hung from a spring is called simple harmonic motion

B. Waves

1. A vibration that extends through time and space

2. All waves are produced by a vibration

3. Waves transfer energy from one place to another, without the transfer of matter.

C. Wave Descriptions

a. Crests – high pointsb. Trough – low points c. Amplitude – maximum displacement from mid point (equilibrium position)

C. Wave Descriptions (continued)

d. wavelength (l, lambda) - distance between two identical points on consecutive waves

1. Measured in meters

C. Wave Descriptions (continued)

e. Frequency (f)1. the number of complete cycles that pass a

fixed point in a given period of time2. one complete vibration (back and forth) is

a cycle3. Unit of measure is called hertz (Hz),

which measures cycles per second- AM radio waves in kiloHertz, FM in MegaHertz

4. The frequency of the vibration causing the wave is the same as the waves frequency

C. Wave Descriptions (continued)

e. Frequency (f)5. Frequency of a wave is inversely

proportional to its periodf = 1/T - this is on your Reference Tables

D. Wave Speed

1. Depends on the medium through which the wave moves.Ex) sound travels through air at speeds of about 330 m/s to 350 m/s in air, depending on temperature- about 4 times faster in water

2. Formula: wave speed = frequency x wavelength

v = f l3. Units: m/s = Hz x m4. this relationship holds true for all waves

Practice Problem

A radio wave (an EM wave) has a frequency of 99.5 MHz and travels at the speed of light, 3.0 x 108 m/s. What is it’s wavelength?

• A sound wave produced by a clock chime 515 m away is heard 1.50 s later.– What is the speed that the wave travels?

– The sound wave has a frequency of 436 Hz. What is its period?

– What is its wavelength?

E. Transverse Waves

1. Particles vibrate perpendicular to the direction that the wave travelsEx) Electromagnetic waves (light, radio)

F. Longitudinal Waves

1. Particles of the medium vibrate parallel to the direction of the waveEx) Sound

II. Wave Interactions

A. Waves at Boundaries Between Media

1. Incident Wave - wave that approaches the boundary

2. Part of energy transmitted into new medium with same frequency (transmitted wave)

3. Remainder of energy bounces back in same media (reflected wave)

4. Differences in Media

i. Small difference→ amplitude of transmitted wave almost as large as incident wave, small reflected wave

ii. Greater difference in media, greater the reflected wave amplitude

iii.When wave passes from less dense medium to a more dense medium, reflected wave is inverted

iv. Transmitted Wave

1. V = x f

2. If speed of wave changes, wavelength must change as well

3. **Frequency remains the SAME

B. Superposition

1. The displacement of a medium caused by 2 or more waves is the sum of the displacements caused by the individual waves

2. Results in Interference

1. Constructive Interference

i. Occurs when wave displacements are in same direction (in phase)

ii. Results in larger amplitude

iii.After interactions of waves they regain their original shape

2. Destructive Interference

a. Occurs when wave displacements are in opposite directions

b. Results in decreased amplitudec. Maximum destructive interference

when waves are 180⁰ out of phase

7. Standing Waves

i. Result from the interference of two waves with equal amplitude and wavelength pass through one another

ii. Nodes remain stationaryiii.Antinodes are positions on a standing

wave with maximum amplitudeiv. Standing waves are set up in the

strings of musical instruments or in the air in organ pipes

Homework

• Read pages 403 – 408• Answer questions p 405 # 1, 2, 3, 5

425 # 62, 63

II. Sound

A. Production

1. Vibration of material objects

2. Cause surrounding medium to vibratea. Considered mechanical waves

because they require a mediumb. Sound waves are longitudinal

3. Freq of source = frequency of sound produced

B. Frequency of Sound

1. Referred to as pitch

2. High frequency, high pitchex) Mosquito ring

3. human range of hearing 20 →20,000 Hz

C. Speed

1. 331 m/s in air @ STP

2. speed changes with changes in temperature (0.6 m/s per

⁰ C)3. speed is different in

different media, the more dense the medium, the faster sound travels

D. Loudness

1. Amplitude of a sound wave

2. measured in decibels3. Relative to the amount of energy

carried by the wave

E. Forced Vibrations

1. Elastic materials can be disturbed and caused to vibrate at its natural frequency, which creates a sound2. Natural frequency – freq at which an object will vibrate with the least amount of energy supplied

Ex) wine glass

3. Resonance

a. Def: the phenomenon that occurs when energy is transferred to a system at its natural frequency

Ex) Tacoma Narrows Bridge

What happens to a sound wave when its source is moving?

F. The Doppler effect1. The apparent change in the frequency of a wave

caused by relative motion between the source of a wave and the observer

2. The greater the speed of the source, the greater the effect

3. As the source moves closer to an outside observer the frequency of the wave increases

a. For sound, pitch increasesb. For light, blue shift

4. As the source moves away from the observer the frequency decreases

Sheldon

Sonic Booms

Light

III. LightA. Early Concepts of Light

1. Travels as waves as evidenced by diffraction

B. Production1. Vibrations of electrons produce

disturbances in electric and magnetic fields

C. Electromagnetic Spectrum

1. The array of electromagnetic waves from shortest to longest

2. The only EM waves that humans can detect are referred to as the visible spectrum (ROY G BIV)

3. The lowest frequency light we see is red.

D. Speed

1. In a vacuum (same in air) = 3.0 x 108 m/s

a. speed of light depends on the medium in which it travels

v = f l

c = f l

What is the relationship between frequency and wavelength?

2. The speed of light depends on the medium in which it travels

3. The ratio of the speed of light in a different medium to the speed of light in a vacuum is given by:

n = c/v

What is the speed of light in a diamond?

E. Behavior of Light1. Reflection

a. Angle of incidence = Angle of reflection

**b. all angles must be measured from the normal line

2. Refraction

a. the bending of light that occurs when a light wave passes through a boundary between two media

b. Result of the change in speed of a wave as it enters a new medium

2. Refraction

a. the bending of light that occurs when a light wave passes through a boundary between two media

b. Result of the change in speed of a wave as it enters a new medium

2. Refraction (continued)

c. The faster the medium, the larger the angle a light ray makes with the normal when it enters the new medium

Example

If light travels faster in fused quartz, what is the correct path of the light?

• If fused quartz is slower?• Fused quartz same speed as Medium X

2. Refraction (continued)

d. Index of Refraction (n)i. If a substance has an index of refraction of 2.00

it means light is twice as fast in a vacuum than it is in that medium

• Which substance slows down light the most when light enters from air?

2. Refraction (continued)

e. Snell's Lawn1sinθ1 = n2sinθ2

1 – incident medium2 – refractive medium

2. Refraction (continued)

i. The light that enters back into the air from the Lucite block bends back out to the same angle that it entered the block

ii. The emerging ray and the incident ray are parallel

3. Diffraction

a. The bending of a wave around a barrier

b. The larger the opening a wave passes through, the less diffraction it experiences

3. Diffraction (continued)

c. The amount of diffraction depends on the size of the wavelength compared to the size of the obstruction

d. The longer the wave compared to the obstruction the greater the diffraction

Double Slit Diffraction

Two speakers, S1 and S2, operating in phase in the same medium produce the circular wave patterns shown in the diagram below.

At which two points is constructive interference occurring?