Journal #20 3/9/12

What type of waves are represented in the diagram below?

What is the main difference between these two types of waves?

A

B

Chapter 14 – Waves and Chapter 15 - Sound

Test will be on Friday, March 23

Vocab Quiz on 3-16-12

Quiz on 3-21-12

Periodic Motion

Motions that repeat in a regular cycle are called

periodic motions.

Examples include:

The blades of a fan moving in a circle

The swinging of a pendulum

The vibrations of a guitar string

Simple Harmonic Motion (SHM)

In simple harmonic motion, an object is pulled out

of its equilibrium position and the resulting force on

the object is directly proportional to the

displacement of the object.

At equilibrium Force required to return to equilibrium

increases with displacement

Vocabulary Check

The amplitude is the MAXIMUM displacement from the equilibrium point. Greater amplitude means that there is a greater intensity or energy in the cycle.

The period is the time it takes for one complete cycle. The symbol for period is T and is measured in seconds.

The frequency is the number of cycles completed in one second. The symbol for frequency is f . Frequency is

measured in units of hertz (Hz), named for Heinrich Rudolf

Hertz(1857–94), a German physicist.

Waves

A wave is a rhythmic disturbance that carries energy through

matter or space.

The particles themselves only vibrate, they do not travel with

the wave.

There are 3 types of waves:

Transverse Wave – a wave that vibrates perpendicular to the

direction of wave motion.

Longitudinal Wave – a wave that vibrates parallel to the

direction of wave motion.

Surface Waves – have the characteristics of both transverse

and longitudinal waves.

TRANSVERSE WAVES

Motion of the particles is perpendicular to wave

direction (energy).

Examples include:

string movements on musical instruments

electromagnetic waves e.g. Light waves, x-rays, radio waves

LONGITUDINAL WAVES

Sound travels as a longitudinal wave (also called a

compressional wave because the particles of

matter are compressed as the wave travels).

Motion of particles is parallel to wave direction

(energy).

SURFACE WAVES

The particles in a surface wave travel in directions

both perpendicular and parallel to the wave

direction (energy).

Picture of a Transverse Wave

Crest

Trough

Wavelength

A

A = Amplitude

Rest

Position

Crest and Trough

Crest – the peak, or highest point, of a wave

Trough (pronounced “troff”) – the lowest point

of a wave

The height of the crest or trough is the

amplitude of the wave.

Wavelength ( )

A wavelength is the shortest distance between

points where the wave pattern repeats itself.

The symbol is the Greek alphabet “Lamda” –

The SI unit for wavelength in meters.

One wavelength can be considered as one cycle of

the wave.

Period and Frequency Revisited

The time it takes one cycle to pass a point is the

period of the wave.

seconds per cycle

The number of wavelengths that pass a point

per second is the frequency of the wave.

cycles per second

seconds

cycle

cycles

second

In symbolic form

or

fT

1

Tf

1

Period and Frequency Practice

What is the frequency of the second hand of a clock?

Period = 60 sec Frequency = 1cycle/60 sec

What is the frequency of US Presidential elections?

Period = 4 yrs Frequency = 1 election/4 yrs

What is the period of AC electricity in the US?

Frequency = 60 Hz Period = 1 sec/ 60 cycles

Calculating Speed of a Wave

Each of these combinations will result in a

distance unit per time unit (m/s usually).

Depending on the wording of the question,

you can set any of these parts equal to

each other to help you solve the question.

Tf

t

dv

Calculating Speed of a Wave Example

Pepe and Alfredo are resting on an offshore raft

after a swim. They estimate that 3.0 m separates a

trough and an adjacent crest of each surface wave

on the lake. They count 12 crests that pass by the

raft in 20.0 s. Calculate how fast the waves are

moving.

Tf

t

dv

Two Important Wave Rules!!

Speed is dictated by the medium (the type of

matter).

Frequency is dictated by the source (the

object creating the vibration).

Homework

Textbook p.398 #75, 76, 78, 80, 81

Journal #21 3/14/12

What factor had the biggest effect on the period

of a pendulum?

Can you explain why the others had almost no

effect at all?

Journal #21 3/14/12

What factor had the biggest effect on the period

of a pendulum?

The length of the string has the greatest effect on the

period of the pendulum. The longer the string, the

longer the period.

Can you explain why the others had almost no

effect at all?

Because gravity pulls on all objects equally, mass nor

angle have a great effect on the period of a

pendulum.

Homework Answers p. 398

75. 8.3s

76. 4.0 m/s

78. a. 0.29 m/s; b. 0.21 s

80. a. 550 Hz; b. 280; c. 170 m

81. 1350 m

Superposition of Waves

Using the principle of superposition, two or more

waves can be combined into a new wave.

The result of the superposition is called interference.

Constructive: when the crest of one wave overlaps the

crest of another; “in phase”.

Destructive: when the crest of one wave overlaps the

trough of another; “out of phase”.

Constructive Interference

Same frequency,

greater amplitude

2 waves in

perfect phase

Complete cancelation,

Zero amplitude

2 waves perfectly

out of phase

Destructive Interference

Notice that the

reflected wave is

inverted

Standing Waves

V

V Standing Wave

V Reflected Wave

V Incident Wave

When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.”

The nodes of a standing wave never move, and the antinodes of a standing wave oscillate up and down.

Standing Waves

There is no

displacement at a

node.

There is maximum

displacement at an

antinode.

Draw the Following Diagram

Journal #22 3/15/12

Determine the number of wavelengths in the

following examples. (hint: some of the examples will

show divisions of ½ of a wave)

Sound travels as a longitudinal wave.

Sounds audible to humans range from 20 - 20,000 Hz.

As frequency increases, pitch rises.

Sound

Loudness of Sound

The amplitude of a sound wave is observed as

loudness.

Loudness is measured in decibels (dB).

Most humans feel pain at about 125 decibels.

Prolonged exposure to sounds of this loudness can

cause permanent damage to the auditory sensory

cells.

Pitch refers to how frequency is observed not speed.

The speed of sound depends on medium and temperature.

The speed of sound in air @ 0 ̊C is 331 m/s. It increases slightly with an increase in temperature.

At room temp, sound travels at 340 m/s.

Speed of Sound

The apparent shift in frequency due to the motion of the object emitting the vibration OR the motion of the person perceiving the sound is called Doppler Shift.

If the sound and the observer are approaching each other, there is an apparent increase in frequency. The opposite is true as well.

Honk! Higher

Pitch

Lower

Pitch

Doppler Shift

How Sound Travels

The blue dot to the right represents a speaker.

The speaker is turned on.

The first sound wave leaves the speaker. No sound is heard yet by the person.

New sound waves emitted and expand outward.

The person hears the sound when the sound waves reaches his ears.

Doppler Shift

Waves closer

together results in

higher pitch

Waves farther

apart results in

lower pitch

Super-sonic Speeds

Traveling at the speed of sound is called

mach 1 (pronounced “mock” 1)

A sonic boom is the loud sound resulting

from the incidence of a shock wave while

crossing the “sound barrier”.

A cone-shaped wave is made by an object

moving at supersonic speed through a fluid.

Sonic Boom Videos

How a Shock Wave Forms

x x x x x x x x x x x x x x x x x x x x x x x x x x x x Pile-up

of

waves

Shock Wave

Journal #23 3/19/12

Complete the following waves with the required

number of wavelengths:

λ = 3½

λ = 2¾

λ = 4½

Frequency and Resonance

The natural frequency of an object is the frequency it

vibrates on its own.

Resonance is a condition that exists when the

frequency of an applied force is the same as the

natural frequency of vibration of an object or system.

Tacoma Narrows Bridge Video

http://videos.howstuffworks.com/tlc/29833-

understanding-tacoma-narrows-bridge-

video.htm

Fundamentals and Harmonics

A fundamental of a string (or object) is the

frequency that matches that objects natural

frequency.

Frequencies that occur at multiples of the

fundamental are called harmonics.

Harmonics of a String

Each end of the string must end in a node!!!

Consonance and Dissonance

Both of these terms are culturally dependent. Some

cultures do not agree with each other on the

pleasantness of certain chords (two or more pitches

played at the same time).

Consonance is when a chord has a pleasing sound.

(Such as a C and an E on a keyboard… called a

“major third”).

Dissonance is when a chord has a displeasing

sound.

Beats

When two notes of similar frequency are played at the same time, the combination of constructive and destructive interference creates audible pattern of loudness and softness called beats. The closer the two notes are in frequency, the slower the beat.

Calculating Beat Frequency

Beat frequency is the number of beats heard per

second when two similar frequencies are sounded

at the same time.

To calculate beat frequency, simply take the

difference of the two similar frequencies.

Example:

What is the beat frequency heard when two tuning

forks frequencies of 440 Hz and 444 Hz are sounded

at the same time?

Journal #24 3/20/12

Use the information provided in the

demo and the diagram to the right to

complete the following questions.

1. How many antinodes appear in the

diagram?

2. If the frequency of the first harmonic is

10.0 Hz, what is the approximate

frequency of this wave?

3. If the frequency of the wave is increased,

what will happen to the wavelength?

Review

What is the highest harmonic shown in the diagram?

If the length of the string is 5 m, what is the wavelength of the 5th harmonic?

If the fundamental frequency is 15 Hz, what is the frequency of the 3rd harmonic?

More Review

Label the following in the diagram below: amplitude, wavelength, crest, and trough.

How many wavelengths are shown in the diagram?

Which variable has the most effect the period of a pendulum: length, mass, or amplitude?

A pendulum takes 10s to complete 2 cycles. What is the period of the pendulum? What is the frequency?

A sound wave has a frequency of 440 Hz and a speed of 340 m/s. What is the wavelength?