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

l

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 (l)

A wavelength is the shortest distance

between points where the wave pattern

repeats itself.

The symbol is the Greek alphabet

“Lamda” – l.

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

secondscycle

cyclessecond

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

yrsWhat 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).

HomeworkTextbook 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. 8.3s76. 4.0 m/s78. a. 0.29 m/s; b. 0.21 s80. a. 550 Hz; b. 280; c. 170 m81. 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.

l

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)

A

B

C

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 xx xxxx x xx xxxxx xxxxxx xx x xxxxPile-up of waves

Shock Wave

Journal #22 3/15/12

Complete the following waves with the required number of wavelengths:

A

B

C

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

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!!

Crystal Goblets Video

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. The closer the two notes are in frequency, the slower the beat.