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Chapter 14: Vibrations and Waves & Chapter 15 : Sound
Objects and Springs:
One of the simplest types of ______________________ is an object attached to a
An object attached to a spring obeys Hooke’s Law:
Where x = displacement
k = spring constant
“-“ means the force is always in the opposite direction of the displacement
In this case, the force on the spring is _______________________________to the amount of
If the object is displaced ___________________ as much, it will feel a force ________ as strong
pulling it back in the other direction.
The restoring force is the force that _________________________________________
An oscillation is the repetitive variation in time of the distance of the object from its equilibrium
Oscillation of a Mass-Spring System
Step 1: The spring is _________________ and released.
Step 2: The spring ___________ the mass back _______________________.
Step 3: The mass _________________ the equilibrium position.
Step 4: The spring is ____________________.
Step 5: The spring __________ the mass back ________________________.
Step 6: and so on and so forth….
Simple Harmonic Motion
Simple harmonic motion occurs when the _____________________________________ to the
displacement from the equilibrium point and is always ______________________________ the
equilibrium point.
In other words, the net force obeys ____________________________.
When two people play catch, does the ball have simple harmonic motion? Why?
Does a mass-spring system turned on its side have simple harmonic motion? Why?
Some Vocabulary
_________________ (A): maximum displacement from equilibrium.
_________________ (T): time it takes to execute a complete cycle of motion
__________________(f): number of cycles or vibrations per unit of time
Unit: Hz = sec-1
Example: A spring is hung vertically and a ______kg object is attached to the lower end of the spring.
When the mass is attached, the spring is stretched _____ cm. What is the spring constant?
The Simple Pendulum
A Simple Pendulum is a system that consists of a _________ attached to a light __________ that
can __________ back and forth.
A simple pendulum is a pendulum that swings at an ________________________. If it is
swinging at more the 15o, it does not display simple harmonic motion.
Equation for the period of a pendulum:
A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is measured. If
the elevator moves with constant velocity, does the period (a) increase, (b) decrease, or (c ) stay the
If the elevator accelerates upward, does the period (a) increase, (b) decrease, (c ) stay the same?
A wave is a disturbance that carries ________________ through __________________ or
Longitudinal Wave – Particles vibrate _________________ to the direction of the wave.
Transverse wave – Particles vibrate __________________ to the direction of the wave.
Defining Terms:
_______________________ : maximum displacement from equilibrium.
________________________:time it takes to execute a complete cycle of motion
______________________:number of cycles or vibrations per unit of time (Hz = sec-1)
________________________: material through which a disturbance travels.
________________________: a wave whose propagation requires a medium.
________________________: a wave whose propagation does not require a medium.
________________________: a single non-periodic disturbance.
________________________: a wave whose source is some form of periodic motion.
________________________: wave pattern that results when two waves of the same f, , and A travel
in opposite directions and interfere.
Draw and label compressions and rarefactions:
Formulas are your friends:
Sample Calculation 1
The string of a piano that produces the note middle C vibrates with a frequency of ________Hz. If the
sound waves produced by this string have a wavelength in air of _____ m, what is the speed of sound in
Sample Calculation 2
What is the period of vibration for an x-ray with a frequency of 3.0 x 1012 ______?
Sample Calculation 3
A tuning fork produces a sound with a frequency of ______________ Hz. The speed of sound in water
is ____________ m/s. Calculate the wavelength produced by this tuning fork in water.
Wave speed depends on the _______________ in the string (F) and the _________________ (m) (mass
of string per unit length) of the string
Another Formula:
Wave interactions/interference:
___________________________: any interference in which waves combine so that the resulting wave
is bigger than the original waves. (Crest meets crest or trough meets trough)
___________________________: any interference in which waves combine so that the resulting wave
is smaller than the largest of the original waves. (crest meets trough)
___________________________: a wave form caused by interference that appears not to move along
the medium and that shows some regions of no vibration (nodes) and other of maximum vibration
Picture of a standing wave:
__________________________: when a wave bounces back off a boundary
Label incident (incoming) and reflected waves.
Free end reflection:
Picture: Incident wave
Reflected wave:
Fixed end reflection:
Picture: Incident wave
Reflected wave:
Chapter 15: Sound
Sound waves are:
_____________________ (requires a medium)
Draw a picture of a longitudinal wave; Label the compressions and rarefactions.
Frequencies of Sound:
Infrasonic Sound (elephants can hear)
Audible Sound (humans can hear)
Ultrasonic Sound (dolphins can detect)
How high or low we perceive a sound to be, depending on the _______________
As the frequency of a sound _______________, the pitch of that sound _______________.
Images produced by __________________ show more detail then those produced with
The _____________ of a sound wave corresponds with how ____________ the sound is.
A ________________ amplitude is a _________________ sound.
A ________________ amplitude is a _________________ sound.
Practice: Draw a sound wave that is:
1) Loud and high pitched.
2)Loud and low pitched.
3) Quiet with medium pitch
Speed of Sound in a medium:
Sound travels fastest in _________________ because ___________________________
_______________________________________ and slowest in ______________ because
Intensity & Decibel Level
Sound waves propagate in 3D
• Sound waves travel away from a vibrating source in all directions.
• In these spherical waves, the circles represent compressions (wave fronts).
__________ (I) of a wave is the rate at which _________ flows through a unit area (A) perpendicular to
the direction of travel of the wave.
• However, ___________ is also the rate at which ______________ is transferred (W = J/sec)
• And sound waves are spherical, so the power is distributed over the surface area of a sphere (4r)
I = Intensity (W/m2)
P = Power (W)
R = Distance from source (m)
Example: What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when
the power output of the trumpet is 0.20 W?
Human Hearing
• The range of human hearing is generally considered to be from about ______ Hz to about 20,000
• In reality, it’s much worse. Few people can hear above 14-15 thousand Hz, and it gets worse as
you grow older.
• Hearing also depends on the ____________ of the sound.
• The softest sound that can be heard by the human ear has an intensity of ________ W/m2. This
intensity is said to be the ________________________.
• The loudest sound the human ear can tolerate has in intensity of _____ W/m2. This is known as
the Threshold of _______________.
• When dealing with human hearing, the intensity range is very large (1x10-12W/m2 to 1W/m2).
• A sound with twice the intensity isn’t heard as twice as loud.
• The ear works on a logarithmic scale.
Sound loudness is measured in ________________ (dB) which compare the sound’s intensity to the
intensity at the threshold of hearing.
Intensity Decibel (dB)
• When the intensity is __________ (one
Threshold of hearing
person talking vs two people talking) there
is a three decibel increase.
Normal Conversation
• When the intensity is
___________________ there is a ten
decibel increase and the noise sounds
Fire Engine
__________ as loud.
Rock Concert
• Example: A rather noisy typewriter
produces a sound intensity of 1 x 10
watts/m which is 70 dB. Find the decibel
level when a second identical machine is added to the office.
Calculating Decibel Level:
 = Decibel Level (dB)
I = Intensity of the sound (W/m2)
Io = 1 x 10-12 W/m2 Threshold of hearing
Example: Ms. Koenig wants to install a 100. W stereo amp in her new VW. What will the dB level be at
her ears which are approximately 1.5 m away from the speakers?
Doppler Effect:
The Doppler effect occurs because relative motion between the _______________ of waves and the
___________________ creates a change in ______________________.
Pictures of the Doppler effect:
How to calculate the change in frequency:
fd = precieved frequency heard by the detector
vd = velocity of the detector
fs = frequency created by the source
vs velocity of the source
* Define the + direction to be
v = velocity of sound
from the source to the detector
Doppler Effect Possibilities:
Example: An ambulance moving at 25 m/s drives towards a physics student sitting on the side of the
road. The EMTs in the ambulance hear the siren sounding at 650 Hz. What is the frequency heard by the
student? (assume speed of sound is 343 m/s)
Example: At rest a car’s horn sounds the note A (_________Hz). While the car is moving down the
street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car’s speed hears a
lower pitched sound.
(A) Is the cyclist ahead of or behind the car?
(B) If the car is moving at 33 m/s (with a horn frequency of 440 Hz) and the bike is following the car at
11 m/s, what is the frequency detected by the bicyclist? (assume speed of sound is 343 m/s)
When an object is moving faster then the speed of sound it is called super sonic. The sound waves pile
up behind the object creating a sonic boom.
Picture of super sonic motion:
When two different frequencies of sound are added together the resulting wave has varying
amplitude. This varying amplitude is heard as beats.
The frequency of the resulting beats can be calculated by: (two different frequencies)
Example: A certain piano key is suppose to vibrate at 440 Hz. To tune it, a musician rings a 440 Hz
tuning fork at the same time as he plays the piano note and hears 4 beats per second. What frequency is
the piano emitting if the note the piano plays is too high?
Beats can also occur from two sources playing the same frequency
Example: Two speakers with the same frequency are placed 3.00 m apart. A listener is originally at
point O, which is located 8.00 m from the center of the line connecting the two speakers. The
listener then walks to point P, which is a perpendicular distance 0.350 m from O, before reaching the
first minimum in sound intensity. What is the frequency of the speakers? (speed of sound in air is
343 m/s)
Standing Waves & Resonance:
The wave pattern that results when two waves of the same f,, and A travel in opposite
directions and interfere.
The ___________________ of the two waves appears to be ___________________.
Resonance is the tendency of a system to vibrate with _________________ at a certain
When a system is in resonance, a small input of _______________ leads to a
Example: Blowing over a bottle of water will produce resonance. If the column of air in the bottle is
____ cm long, what is the resonant frequency of the bottle? (assume vsound = 343 m/s)
The water stops the sound so it is a node.
The air is free to move at the top of the bottle, so it is an antinode.
Going from node to the first antinode, is ¼ of a wave.
Therefore, the length of the bottle is ¼th the wavelength.
Example: Resonance in a tube: Tuning fork with frequency of 958 Hz. What is the length (L) of tube out
of the water? (Assume the speed of sound is 345 m/s.)
Sometimes more than one size wave will fit the given parameters. These different wave sizes are
called _________________.
First harmonic (or fundamental frequency) is the ______________ wave that fits the parameters.
_____________ harmonic (first overtone) is the second largest wave that fits the parameters.
1st Harmonic:
2nd Harmonic:
3rd Harmonic:
Types of Parameters:
Tube with two open sides
1st Harmonic:
2nd Harmonic:
3rd Harmonic:
Tube one side closed
1st Harmonic:
2nd Harmonic:
3rd Harmonic:
String 2 fixed ends (tube, 2 closed ends)
1st Harmonic:
2nd Harmonic:
3rd Harmonic: