Waves Unit / Mechanical Waves Sub-Unit Regents Physics Notes - 5-1 Mech Waves Sub-Unit.pdf · Waves Unit / Mechanical Waves Sub-Unit Regents Physics 1 | P a g e 5.1.1 Oscillations

Waves Unit / Mechanical Waves Sub-Unit Regents Physics

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5.1.1 Oscillations

• _______________________ - time for one oscillation

• _______________________ - number of oscillations per second

PRACTICE

1. A pendulum is timed as it moves from its starting point “A” to several other positions as it swings.

a. Use the data from the position/time chart to determine the period of the

pendulum. _________s

b. Calculate the frequency of the pendulum.

c. Use the period of the pendulum to calculate the length of the pendulum string.

2. A spring and mass system has a period of 0.45 seconds. The spring constant of the spring is 300 newtons per meter. Determine the amount of mass on the spring.

start start

Pendulum Mass on a Spring

Equation Equation

Equation

D

E

C B

A L

Position Elapsed

Time

A 0.00 s

B 0.20 s

C 0.40 s

D 0.60 s

E 0.80 s

- Four pendulums are built as shown in the table below:

Pendulum Mass Length

A M L

B 2M L

C M 2L

D 2M 2L

o Which statements below are true?

(a) Pendulums A and B have the same period. (b) Pendulums A and C have the same period. (c) Pendulums C and D have the same period. (d) Pendulums B and D have the same period. (e) Pendulum A has a shorter period than pendulum B. (f) Pendulum A has a shorter period than pendulum C.

[a, c, f]

- Four masses are hung on four springs as shown in the table below:

System Mass Spring Constant

A M k

B M 2k

C 2M k

D 2M 2k

o Which statements below are true?

(a) Systems A and B have the same period. (b) Systems A and C have the same period. (c) Systems A and D have the same period. (d) System A has the shortest period. (e) System B has the shortest period. (f) System C has the shortest period.

[c, e]

Review Questions

5.1.1 – Explain the relationship between the period of a pendulum and the factors involved in building one. Explain the relationship between the period of a mass oscillating on a spring and the factors involved in building one.

- How long does it take for a pendulum with a frequency of 2.0 hertz to complete one full oscillation?

[0.5s]

- Determine the period of a pendulum with a length of 40 centimeters.

[1.3s]

- An astronaut notes that on planet P it takes 1.5 seconds for a pendulum with a

length of 0.50 meter to complete one full oscillation. What is the acceleration due to gravity on planet P?

[8.8m/s2]

- A 2.0 kilogram mass is hung on a spring with a spring constant of 100 newtons per meter.

o What period will the mass oscillate back and forth with?

[0.9s]

o What frequency will this oscillation have?

[1.1Hz]


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5.1.2 Pulses

Definitions

• _______________________ - a single vibratory disturbance Transmits ENERGY but not MASS

• _______________________ - height above equilibrium and directly related to

ENERGY.

• _______________________ - a continuum of particles of the same type that stores and releases energy.

• As a pulse travels in a medium it…

o ____________________________________________________

o ____________________________________________________

Phenomenon #1 - Reflection

• If a pulse changes mediums it…

o ____________________________________________________

o ____________________________________________________

Phenomenon #2 - Interference

before

after

before

after

Fixed Point Floating Point

Fast Slow Slow Fast

before

after

before

after

Constructive Destructive

PRACTICE

1. Sketch a pulse that shows the superposition of the pulse pairs below.

2. A pulse with a height of +0.5 meter encounters a second pulse with a height of +2.3

meters.

a. The two pulses interfere: ___________________________

b. The resulting height of the medium when the pulses interfere will be: ______________ m

3. A pulse with an amplitude of 0.4 meter moves from a thick, heavy cord where its speed is 2.0 meters per second into a much thinner string. The speed and height of the pulse after it is transmitted could be:

(1) Amplitude = 0.5 m; Speed = 1.0 m/s (2) Amplitude = 0.3 m; Speed = 1.0 m/s (3) Amplitude = 0.5 m; Speed = 3.0 m/s (4) Amplitude = 0.3 m; Speed = 3.0 m/s

Review Questions

5.1.2 – Explain the definition of a pulse. Explain reflection and superposition of pulses.

- Which of the following is transmitted by a pulse? (1) energy and mass (2) mass only (3) energy only

- The energy contained in a pulse is related to its:

(1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only

- As pulses travel they lose:

(1) amplitude and speed (3) width and speed (2) amplitude only (4) speed only

[3; 2; 2]

- A pulse moves from a very thick rope into a thin string. Circle the term that

makes the statement true.

(a) The transmitted pulse will lose / gain amplitude.

(b) The transmitted pulse will lose / gain speed.

(c) The transmitted pulse will lose / gain energy.

(d) The reflected pulse will / will not come back on the opposite side.

[gain; gain; lose; will not]

Sketch the superposition of the following sets of pulses.

Amp = +1

Amp = +1

Amp = -0.5

Amp = +3

Amp = -2

Amp = +2

Amp = -1

Amp = +1


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5.1.3 Wave Properties

Definitions and Types of Waves

• _______________________ - a regularly repeating pulse.

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

Longitudinal Wave – particles of the medium move ____________________ to the wave’s

direction of travel.

Wave Velocity Waves have a definite direction of travel.

Wave period (T) = ___________________________________________

Wave frequency (f) = ________________________________________

IMPORTANT: ONCE A WAVE IS PRODCUED ITS FREQUENCY CANNOT BE CHANGED!

Wavelength (λ)= ____________________________________________

Because frequency is always the same, if a wave changes speed (mediums), its wavelength

must also change.

Example

- A wave with a frequency of 1.5 hertz is moving through a heavy spring where its wavelength is 2.0 meters.

o What is the speed of this wave?

o What wavelength would the wave have if it moved into a lighter spring where its speed was 6.0 meters per second?

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

Equation

___________________

________________ λ

Motion of particles in the medium

v

Motion of particles in the medium

____________

___________

A

λ v

Wave Phase

What is the direction of motion in the medium?

Two points are considered to be “in phase” if they are moving in the same direction at the same time. The number of degrees “out of phase” depends on the difference in wavelength between the points. 0° = ____________________________ 90° = ___________________________ 180° = __________________________

PRACTICE

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

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

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

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

A

B

C

D

E

F F

v

v v


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

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

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

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

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

- What is the wavelength of each of the waves shown below?

[2m; 6m; 4m; 0.8m; 3m]

2 m

12 m

6 m

0.4 m

4.5 m

a. b.

c. d.

e.

Review Questions

5.1.3 – Use equations to determine wave speed, wavelength, period, or frequency. Understand the difference between longitudinal and transverse waves. Explain how amplitude and wavelength are measured. Explain the concept of ‘phase’. Explain the direction of particle motion in a medium.

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

[30m/s]

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

[5m]

- 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?

[2Hz; 0.5s]

5.1.4 Interference, Standing Waves, and Resonance

Introduction and Terms

• _______________________ - the result of two waves meeting in a medium.

o ___________________________ - results in greater amplitude.

o ___________________________ - results in lower amplitude.

• “In phase” interferes _________________________________

• “180° out of phase” interferes __________________________

• Between 0° and 180° results in different amounts of interference at different points.

- What is the amplitude of each of the waves shown below?

[0.25m; 2m]

0.5 m 2.0 m

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

[BD; AB,BC; AC,BD]

A

B

C

D

- 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.

[↓↑↑↓↑]

A

B

C

D

v

ED

- 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

[2]

- How will particle A move in the wave shown below?

(1) (3)

(2) (4) [3]

A


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Interference of Two Point Sources of Waves

Phenomenon #3 - Standing Waves

• When a wave encounters a fixed boundary it _________________________.

• The reflected wave comes back through the original wave and they ____________________________.

• The result is a standing wave

o Standing wave features:

__________________________ : always 180° out of phase (destructive interference) - NO MOTION.

___________________________ : alternate between in-phase and 180° out of phase –MAX MOTION.

Phenomenon #4 - Resonance

All mediums have a __________________________________ that corresponds to their atomic structure.

• Exciting this frequency causes large ______________________ vibrations in the medium

• If the frequency is excited with enough ______________________ the medium may become damaged or even shatter.

• If two materials have the same (or close) natural frequencies then vibrations may be passed from one material into the other.

PRACTICE

1. The grid below represents a 10.0 meter long string.

a. Sketch the standing wave that this string would produce if it were to have

SIX nodes.

b. Draw a circle around each ANTINODE on the string.

c. Determine the wavelength of this standing wave. _________________m

d. Assuming that this wave moves at 2.0 meters per second, calculate its frequency and period.

crest (wave front)

trough

A standing wave is produced as a result of a combination of

___________________ and ______________________.

The main features of standing waves are:

______________________ at which minimum motion of the medium occurs. _______________________ at which maximum motion of the medium occurs. Determine the wavelength of the standing wave shown below. Identify one node and one anti-node.

5.0 m

- A (NODE/ANTINODE) is the result of an alternating phase difference of 0 and 180 degrees between two waves passing through each other. (Circle one)

- To produce a standing wave, two waves must:

o be moving in _______________________________

o have the same:

_____________________________

_____________________________

_____________________________

[reflection, interference; node, anti-node] [2.5m]

[anti-node] [same direction; amplitude, frequency, wavelength]

Review Questions

5.1.4 – Explain the phenomenon of wave interference. Explain the origin of and describe features of standing waves. Explain the phenomenon of resonance.

- Two point sources produce a pattern of overlapping circular waves. The solid lines in the diagram represent wave crests while the dotted lines represent wave troughs. Mark a “C” in the boxes that inidcate constructive interference and a “D”in the boxes that indicate destructive interference.

- Sketch a wave that will completely destructively interfere with the wave shown below. What is the phase difference between these two waves?

- At the point when the two waves shown below completely overlap, what will the superposition of the two waves look like? Draw a sketch of the wave produced during this interaction.

v v


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5.1.5 Sound and Doppler Effect

Sound Facts

• Sound is transmitted as a _______________________ wave.

• Mechanical wave so it requires ________________________________.

• Speed of sound in…

o air: _____________________________ m/s

o sea water: ________________________ m/s

o steel: ____________________________ m/s

• Amplitude of a sound wave is synonymous with

___________________________________________________________

Phenomenon #5 – Doppler Effect

• A source sends out waves in all directions with the same frequency and

wavelength.

• How the wave is perceived by an observer depends on

______________________________ of the source and/or observer.

o Same frame of reference

o Getting closer together - __________________________

…at increasing speed - ________________________

…at decreasing speed - ________________________

o Getting farther apart - ____________________________

…at increasing speed - ________________________

…at decreasing speed - ________________________

PRACTICE

1. What is the frequency of a sound wave with a wavelength of 0.04 meter in air? What type of wave is this, transverse or longitudinal?

2. A bat is using sound waves to locate an insect. The bat produces sounds with a frequency of 120 kilo-hertz and notes that the sound it transmits echo’s back in 0.02 second.

a. What is the bat’s distance to its prey? b. What is the wavelength of the bat’s radar?

3. A radar station is tracking a dense section of cloud cover. If the radar station

transmits energy at a frequency of 300 megahertz and receives reflected energy from the clouds at a frequency of 150 megahertz, what can the forecasters say about the motion of the clouds?

- Circle the terms that properly complete the sentences below.

o Sound is transmitted as a TRANSVERSE / LONGITUDINAL wave.

o Sound is produced as a(n) MECHANICAL / ELECTROMAGNETIC wave.

o Sound travels more QUICKLY / SLOWLY in water than it does in air. Explain why this is true!

- The diagram below shows a source of sound waves moving with a constant speed near an observer. The source produces sound waves with a frequency of 100 hertz.

o Is the source getting closer to the observer or farther away?

o Which frequencies could the observer be hearing as the source approaches?

(a) 80 Hz (b) 100 Hz (c) 110 Hz (d) 120 Hz

o As the source approaches, will the frequency heard by the observer be constant, increasing, or decreasing?

[longitudinal; mechanical; quickly – density] [closer; (d); constant]

Observer

Review Questions

5.1.5 – Explain the origin of sound waves, the conditions necessary for them to exist and details regarding their transmission. Explain the motion of objects in Doppler Effect diagrams. Explain frequency changes due to the Doppler Effect.

- If a ship sends a sonar signal through the water to the sea floor and it bounces back to arrive back at the ship in 2.0 seconds, how deep is the water under the ship if sound travels through water at 1500 meters per second?

[1500m]

- If it takes a sound wave 2.5 seconds to travel from the spot where a

lightning strike occurs to an observer, how far away from the observer did the strike occur?

[828m]

- Why would an astronaut not be able to communicate with another

astronaut by talking in the vacuum of space?

[no medium to conduct the sound]


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5.1.6 Diffraction, Reflection, and Refraction

Huygen’s Principle

• ______________________________ - a small source of circular waves. o Lined up next to one another they will produce a…..

• ______________________________ - represents a wave crest.

o The direction in which these travel is shown by a….

• ______________________________ - shows the direction of a wave’s travel.

Phenomenon #6 - Diffraction

• When a barrier blocks part of a wave-front only part of the wave will pass.

• Because a wave-front is a collection of wavelets, the wavelet on the corner of the barrier will be able to express its curvature.

• This causes the way-rays to _________________________________________

Single-Opening Diffraction

• When a wave front passes through an opening in a barrier the wave rays bend around BOTH corners.

• The amount of bending depends on the relationship between

______________________ and ___________________________

Wavelength << Opening Size Wavelength ≈ Opening Size

- A train is moving at a constant 35 meters per second away from an observer. As the train is moving it blasts its horn which produces a sound with a frequency of 1000 hertz. The observer will perceive that the horn’s frequency is

(1) less than 1000 hertz and constant (2) less than 1000 hertz and decreasing (3) greater than 1000 hertz and constant (4) greater than 1000 hertz and increasing

- A police car is accelerating toward an observer. The police car’s siren produces a sound with a frequency of 1200 hertz. The observer will perceive that the siren’s frequency is

(1) less than 1200 hertz and constant (2) less than 1200 hertz and decreasing (3) greater than 1200 hertz and constant (4) greater than 1200 hertz and increasing

[1; 4]

Double-Slit Diffraction

• When a wave-front passes through two slits at the same time it bends through both slits and the wave-fronts interfere.

Reflection Revisited

Phenomenon #7 - Refraction

Phenomenon #8 – Polarization

A polarizer only allows waves with particles vibrating in a specific direction to pass.

This only works for _______________________ waves.

When a wave-ray passes from one medium into another it will bend

due to the difference in

________________________ between the two mediums.

Slow medium Fast medium

Bends ______________

λ ______________

Fast medium Slow medium

Bends ______________

λ ______________

Regular (Specular) Diffuse


15 | P a g e

PRACTICE

1. A wave with a wavelength of 3.0 meters passes through an opening that is 0.02 meters wide. Which statement best describes what will happen to the wave?

(1) The wave fronts will not bend. (2) The wave fronts will bend to a large degree. (3) The wave fronts will bend, but only slightly. (4) The wave will be completely stopped and will not pass.

2. Which combination will produce the least degree of diffraction?

(1) a wavelength of 2.0 m through an opening of 1.0 cm (2) a wavelength of 30 m through an opening of 2.0 m (3) a wavelength of 2.0 m through an opening of 25 m (4) a wavelength of 5.0 nm through an opening of 45 m

3. Which wave phenomenon relates to…

a. apparent bending of a pencil in a cup of water.

b. bouncing of light off of a mirror.

c. bending of water waves as they pass a dock.

d. selective filtering of light passing through sunglasses.

e. apparent change in frequency due to a moving source.

f. production of nodes and anti-nodes.

g. vibrations produced at a medium’s natural frequency.

h. meeting of two waves in a medium.

Review Questions

5.1.6 – Describe the phenomenon of reflection; identify and sketch wave front diagrams in which reflection occurs. Explain why waves refract; identify and sketch wave front diagrams in which refraction occurs. Explain the diffraction of waves. Identify and sketch wave front diagrams in which diffraction occurs.

- When waves encounter a change in medium or a barrier, some of the energy is always ____________________ and some is always _____________________.

- The diagram below shows a series of wave fronts approaching a barrier. Sketch a set of reflected wave fronts on the diagram.

[reflected, transmitted]

- Waves refract when they change ____________________.

- In which area of the diagram below is the wave traveling more quickly?

[speed/direction; area 1]

Area 1

Area 2

- Waves are diffracted as they pass through openings or around barriers. Sketch the diffraction pattern in each of the three cases shown below. In which case is the diffraction most pronounced?

[right diagram is most pronounced]

Documents

Waves Unit / Mechanical Waves Sub-Unit Regents Physics Notes - 5-1 Mech Waves Sub-Unit.pdf · Waves Unit / Mechanical Waves Sub-Unit Regents Physics 1 | P a g e 5.1.1 Oscillations