Chapter 13: Vibrations and Waves

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 ______.

______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….

Think: What does oscillation mean?

Simple Harmonic Motion

______occurs when the net force along the direction of motion ______.
In other words, simple harmonic motion is when the ______to the displacement from the equilibrium point and is always ______the equilibrium point.

When two people play catch, does the ball have simple harmonic motion? Why?

Does a mass-spring system turned on it’s side have simple harmonic motion? Why?

Some Vocabulary

Amplitude (A): maximum displacement from equilibrium.
Period (T): time it takes to execute a complete cycle of motion
Frequency (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 same?

If the elevator accelerates upward, does the period (a) increase, (b) decrease, (c ) stay the same?

Waves

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.

WAVE ANATOMY:

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 air?

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 Friendly 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 (antinodes).

Picture of a standing wave:

______: when a wave bounces back off a boundary

Label incident (incoming) and reflected waves.

Free end reflection: The loop is free to move upward on the pole. Then the downward component of the ______in the string makes the loop go back down creating the ______pulse.

The pulse is ______as it came in.

Fixed end reflection: As the pulse hits the wall, the pulse pushes up on the wall. The ______(Newton’s 3rd law). This causes the pulse to ______.

The pulse is reflected back exactly as it came in, only inverted.

Chapter 14: 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)

Pitch

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 ______.

Amplitude

The ______of a sound wave corresponds with how ______the sound is.

A ______amplitude is a ______sound.
A ______amplitude is a ______sound.

Practice:

Draw a loud and high pitched wave.

Draw a loud and low pitched wave.

Draw a quiet sound wave with medium pitch

Speed of Sound:

Sound travels fastest in ______because ______and slowest in ______because ______.

To find a table of the speed of sound in different mediums, look on p. 461 in the textbook.

Sound waves in 3D:

Sound waves travel away from a vibrating source in ______.
In these spherical waves, the circles represent ______or ______.
Labeled diagram:

Intensity:

Intensity (I) of a wave is the rate at which energy flows through a unit area (A) perpendicular to the direction of travel of the wave.

General Equation:Spherical Waves centered on the source:

Units: Watts/m2, W/m2

To compare the sound intensities at different distances, use this equation:

Relative Loudness – Decibels (dB)

Decibels are designed for talking about numbers of greatly different order of magnitudes.
Such as….1 and .000000000001
For convenience the ______between the two numbers is converted into a ______. Logarithms are used because the human ear responds to sound roughly in a logarithmic manner.
Doubling the sound intensity is a 3 dB increase.

To calculate the dB level (b):

Where Io = 10-12

Threshold of hearing = 0 dB; Threshold of pain = 120 dB

Example: A rather noisy typewriter produces a sound intensity of ______. Find the decibel level of this machine and calculate the new decibel level when a ______identical machine is added to the office.

Example: Ms. Monson wants to install a _____ W stereo amp in her new VW.

a. What will the dB level be, at her ears, approximately ______away from the speakers?

b. At what distance will her music be reduced to a mere whisper, (______)?

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:

+vobserver when the observer is moving toward the source

-vobserver when the observer is moving away from the source

+vsource when the source is moving toward the observer

-vsource when the source is moving away from the observer

Example: At rest a car’s horn sounds the note A (______). 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 the note A-flat (______).

Is the cyclist ahead or behind the car?

How fast is the car moving?

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:

Beats:

When two different frequencies of sound are added together the resulting wave has varying amplitude. This varying amplitude is heard as beats.

______occurs when sound waves from two sources cancel each other out. No sound is heard with destructive interference.

______occurs when sound waves from two sources add together to create a louder sound (or higher amplitude wave).

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 found intensity. What is the frequency of the speakers? (speed of sound in air is 343 m/s)

Standing Waves:

The wave pattern that results when two waves of the same f, l, 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: 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.)