Waves Class Notes - Hicksville Public Schools / Homepage

Review:
1. A ball dropped from rest falls freely until it hits the ground with a speed of 20 meters per second. The time during which the ball is in free fall is approximately
2. In a flashlight, a battery provides a total of 3.0 volts to a bulb. If the flashlight bulb has an operating resistance of 5.0 ohms, the current through the bulb is
Transverse Waves
The vibration or motion of a particle is perpendicular to the motion of the wave
Examples of transverse waves: Ocean waves, Electromagnetic (EM) waves, strings
Waves
Waves transfer energy without transferring matter
A pulse is a single disturbance
A periodic pulse creates a wave
Two groups of waves
1. Mechanical waves – sound, ocean waves, etc.
2. Electromagnetic waves – light, radio, microwaves, x rays, etc.
Waves can be transverse or longitudinal
Longitudinal Waves
The vibration or motion of the particle is parallel to the motion of the wave
Examples of longitudinal waves: Sound
Longitudinal Waves
Compression
Rarefaction
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Characteristics of periodic waves
Period – Speed of a wave – Frequency – Amplitude – Wavelength – 1. What is the period of a 60.­hertz electromagnetic wave traveling at 3.0 × 108 meters per second?
2. A wave completes 5 cycles in 2 seconds over a dista
nce of 3m. a) What is the wavelength?
b) What is the frequency?
c) What is the period?
d) What is the speed of the wave?
3. What is the frequency of a wave with a wavelength of 500 meters if it travels at a velocity of 25 meters per second? What is its period?
Page 5 review questions 6­7
6. What is the magnitude of the centripetal force on a 2 x 103 kg car as it goes around a 25 meter curve with an acceleration of 5 m/s2?
7. A 0.5 kg ball is thrown vertically upward with an initial kinetic energy of 25 joules. Approximately how high will the ball rise?
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Simple Harmonic Motion – Masses go to and fro
Oscillation – a periodic variation from one state to another
Simple harmonic oscillator – an object that repeats a period motion
Potential energy
Kinetic energy
Total Energy
Question:
A pendulum completes 10 swings in 15 seconds.
What is the period (T) of the pendulum in seconds?
What is the frequency (f) of the pendulum in Hz?
Pulses – Wave Building Blocks
A pulse is a single vibratory disturbance that transfers energy but NOT mass.
Question:
A mass on a spring oscillates at 3.2 Hz.
What is the period of the system (in seconds)?
Amplitude is the height of a pulse above equilibrium – shows ENERGY
How long will it take the system to complete 120 oscillations?
The medium stores then releases energy as pulses travel through it.
A medium is a continuum of particles of a single type
ex: Water, air, metal rod, etc.
Pulse
Periodic Wave
When pulses change mediums, they are
Interference
Pulses that encounter one another in a medium interfere
Pulse amplitudes are added together using the principle of superposition
Two types of interference:
Constructive Interference
Occurs when amplitude of two pulses is in the same direction
Energy of the two pulses is added together to produce a higher amplitude
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Page 7 review questions 8­9
Destructive Interference
Occurs when pulse amplitudes are in opposite directions
ENERGY of the two pulses partially or completely cancel out to produce a lower amplitude.
8. If 10 coulombs of charge are transferred through an electric circuit in 5.0 seconds, then the current in the circuit is 9. In driving down a hill a car loses 500 joules of potential energy but gains 1500 joules of kinetic energy. If the work done to overcome friction was 200 joules, determine the total work done by the engine to go down the hill.
Sound Waves
A speaker pushes air forward and backward. The sound wave travels until it reaches your ear. What type of wave is the sound wave?
Through what medium is the sound travelling?
What would happen to a sound wave in a vacuum?
The amplitude of the sound wave is also the:
Are the air molecules that bounce off the speaker the same ones that reach your ear?
Sound travels through air at 331 m/s
Sound travels faster through denser mediums:
Speed of sound in water Speed of sound in steel
Humans can hear sound from 20 Hz to 20kHz. Frequency = Which strings will have a longer wavelength?
v = f λ
Which will have a higher pitch?
What happens to the wavelength when you make a trombone longer?
What happens to the pitch?
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1. At STP, sound with a wavelength of 1.66 meters has a frequency of:
4. If the speed of a wave doubles, its wavelength will be:
2. Middle C has a frequency of 262 Hz. What is the 5. What is the period of a sound wave with frequency wavelength of middle C in air?
600 Hz?
3. What is the wavelength of middle C in water?
6. If the period of a sound wave is doubled, its frequency will be:
­2 s is travelling 7. A sound wave with period 5.5 x 10
through the air. What is the wavelength of the sound wave?
9. You see lightning, and 5 seconds later you hear thunder. How far away from you did the lightning strike?
10. Mr. Vigneaux yells “Echo” across the grand canyon. 2.5 seconds later, he hears his echo. What is the width of the canyon where he is yelling? 8. How much time does it take light from a flash camera to reach a subject 6.0 meters across a room?
Page 11 review questions 21­22
21. When 800 joules of work ar done on an object, its potential energy increases by 300 joules and its kinetic energy increases by 400 joule. What was the work done against friction?
22. In a seris circuit containing two lamps, the battery supplies a potential difference of 1.5 volts. If the current in the circuit is 0.1 amperes, at what rate does the circuit use energy?
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Wave Interference
Waves are superimposed like pulses
Resonance
•Resonance occurs when a medium is vibrated near its _________________________
•Constructive interference occurs to an extreme degree causing vibrations with huge amplitude
•If the vibration has enough energy and the correct frequency, the medium may be damaged or destroyed!
Examples of resonance:
• When you push somebody on a swing, you push with the same frequency as the swing to get maximum amplitude
• Color is due to incoming light matching the natural frequency of electrons orbiting the proton in an atom
• Instruments create a standing wave at a natural frequency to create a note. Some instruments allow you to change the length of the instrument to change the frequency and allow more notes!
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Page 13 review questions 23­24
23. What is the approximate electrostatic force between two protons separated by a distance of 1.0 x 10­6 m?
Wave Fronts
A wave front is made up of all points on a wave that are vibrating in phase (in unison)
Wave fronts are separated by one wavelength.
24. What is the total resistance of the circuit?
Rays can be used to represent the direction that a wave is travelling in. Rays are drawn perpendicular to wave fronts.
The Doppler Effect
The apparent change in the _____________________ of a wave when the source and observer are moving relative to one another
• When the source and observer are approaching each other, the observed frequency is _____________
than the actual frequency of the wave.
• When the source and observer are moving away from each other, the observed frequency is ______________ than the actual frequency of the wave.
• Note that this change in frequency is only apparent. The actual frequency of the wave depends only on the ___________________
• For light the Doppler shift is observed as a __________________ (higher apparent frequency) or ________________ (lower apparent frequency
All waves that reach a boundary can be reflected, refracted (transmitted), absorbed, and/or scattered.
Reflection
A wave that reaches a boundary can be reflected
Light – mirror
Sound – echo
Law of reflection: (NOTE: All angles are measured from the normal to the surface)
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Refraction (transmission)
When a wave enters a new medium, there is a change in angle of the wave due to the change in speed.
Medium is the material through which a wave is travelling (air, glass, water, etc.)
Fast medium to slow medium
Wave bends
Slow medium to fast medium
Wave bends
Wave incident along the normal – change in ______________ but no change in _____________
Change in speed of the wave results in a change in _____________________. The ____________________ of the wave is unchanged! (Depends only on the source creating the wave)
Diffraction
The _____________ of a wave to travel around corners, obstacles, or openings in its path
How much a wave diffracts depends on how the wavelength compares to the size of the opening (smaller opening, more diffraction)
Huygen’s Principle: Every point on the wave acts as a new point source
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