Waves and Sound

Mechanical Wave

A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium.

Wave “Pulse”

Water Waves

Animation courtesy of Dr. Dan Russell, Kettering University

People Wave

Parts of a Wave

3

-3

2 4 6 x(m)

y(m)

A: amplitude

: wavelength crest

trough

equilibrium

Speed of a wave

The speed of a wave is the distance traveled by a given point on the wave (such as a crest) in a given interval of time.

v = d/t d: distance (m) t: time (s)

v = ƒ v : speed (m /s) : wavelength (m) ƒ : frequency (s–1, Hz)

Period of a wave

T = 1/ƒ

T : period (s)

ƒ : frequency (s-1, Hz)

Problem: Sound travels at approximately 340 m/s, and

light travels at 3.0 x 108 m/s. How far away is a lightning

strike if the sound of the thunder arrives at a location 2.0

seconds after the lightning is seen?

Problem: The frequency of an oboe’s A is 440 Hz. What

is the period of this note? What is the wavelength?

Assume a speed of sound in air of 340 m/s.

Types of Waves

Refraction and Reflection

Wave Types

A transverse wave is a wave in which particles of

the medium move in a direction perpendicular to

the direction which the wave moves.

Example: Waves on a String

A longitudinal wave is a wave in which particles

of the medium move in a direction parallel to the

direction which the wave moves. These are also

called compression waves.

Example: sound

http://einstein.byu.edu/~masong/HTMstuff/WaveTrans.html

Wave types: transverse

Wave types: longitudinal

Longitudinal vs Transverse

Other Wave Types

Earthquakes: combination

Ocean waves: surface

Light: electromagnetic

Reflection of waves

• Occurs when a wave strikes a medium boundary and “bounces back” into original medium.

• Completely reflected waves have the same energy and speed as original wave.

Reflection Types

Fixed-end reflection: The wave reflects with inverted phase.

Open-end reflection: The wave reflects with the same phase

Animation courtesy of Dr. Dan Russell, Kettering University

Refraction of waves

• Transmission of wave from one medium to another.

• Refracted waves may change speed and wavelength.

• Refraction is almost always accompanied by some reflection.

• Refracted waves do not change frequency.

Animation courtesy of Dr. Dan Russell, Kettering University

Sound is a longitudinal wave

Sound travels through the air at approximately 340 m/s.

It travels through other media as well, often much faster than that!

Sound waves are started by vibration of some other material, which starts the air moving.

Animation courtesy of Dr. Dan Russell, Kettering University

Hearing Sounds

We hear a sound as “high” or “low” depending on its frequency or wavelength. Sounds with short wavelengths and high frequencies sound high-pitched to our ears, and sounds with long wavelengths and low frequencies sound low-pitched. The range of human hearing is from about 20 Hz to about 20,000 Hz.

The amplitude of a sound’s vibration is interpreted as its loudness. We measure the loudness (also called sound intensity) on the decibel scale, which is logarithmic.

© Tom Henderson, 1996-2004

Calculating Sound Intensity

β = 10 log I / Io

β is sound level in decibels (dB)

I is the sound intensity (W/m2 )

Io is the threshold of hearing, minimum

sound intensity perceived by the ear.

Io = 1 x 10-12 W/m2

Doppler Effect The Doppler Effect is the raising or lowering of the perceived pitch of a sound based on the relative motion of observer and source of the sound. When a car blowing its horn races toward you, the sound of its horn appears higher in pitch, since the wavelength has been effectively shortened by the motion of the car relative to you. The opposite happens when the car races away.

Doppler Effect

Stationary source

Moving source

Supersonic source Animations courtesy of Dr. Dan Russell, Kettering University

http://www.kettering.edu/~drussell/Demos/doppler/mach1.mpg

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

Doppler Equation

Use the top signs when

approaching & bottom

sign when receding

Pure Sounds

Sounds are longitudinal waves, but if we graph them right, we can make them look like transverse waves.

When we graph the air motion involved in a pure sound tone versus position, we get what looks like a sine or cosine function.

A tuning fork produces a relatively pure tone. So does a human whistle.

Later in the period, we will sample various pure sounds and see what they “look” like.

Graphing a Sound Wave

Complex Sounds

Because of the phenomena of “superposition”

and “interference” real world waveforms may not

appear to be pure sine or cosine functions.

That is because most real world sounds are

composed of multiple frequencies.

The human voice and most musical instruments

produce complex sounds.

Superposition of Waves

Principle of Superposition

When two or more waves pass a particular

point in a medium simultaneously, the

resulting displacement at that point in the

medium is the sum of the displacements

due to each individual wave.

The waves interfere with each other.

Types of interference.

If the waves are “in phase”, that is crests and troughs are aligned, the amplitude is increased. This is called constructive interference.

If the waves are “out of phase”, that is crests and troughs are completely misaligned, the amplitude is decreased and can even be zero. This is called destructive interference.

Constructive Interference

crests aligned with crest

waves are “in phase”

Constructive Interference

Destructive Interference

crests aligned with troughs

waves are “out of phase”

Destructive Interference

Sample Problem: Draw the waveform from

its two components.

Sample Problem: Draw the waveform from

its two components.

Standing Waves

Standing Wave

A standing wave is a wave which is reflected back and forth between fixed ends (of a string or pipe, for example).

Reflection may be fixed or open-ended.

Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave.

Let’s see a simulation.

Fixed-end standing waves

(violin string)

1st harmonic

2nd harmonic

3rd harmonic

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html

Animation available at:

Fixed-end standing waves

(violin string)

Fundamental First harmonic = 2L

First Overtone Second harmonic = L

Second Overtone Third harmonic = 2L/3

L

Open-end standing waves

(organ pipes)

Fundamental First harmonic = 2L

First Overtone Second harmonic = L

Second Overtone Third harmonic = 2L/3

L

Mixed standing waves

(some organ pipes)

First harmonic = 4L

Second harmonic = (4/3)L

Third harmonic = (4/5)L

L

Sample Problem

How long do you need to make an organ pipe that produces a

fundamental frequency of middle C (256 Hz)? The speed of the sound

in air is 340 m/s.

A) Draw the standing wave for the first harmonic

B) Calculate the pipe length.

C) What is the wavelength and frequency of the 2nd harmonic?

Draw the standing wave

Resonance and Beats

Sample Problem How long do you need to make an organ pipe whose fundamental

frequency is a middle C (256 Hz)? The pipe is closed on one end, and the speed of sound in air is 340 m/s.

A) Draw the situation.

B) Calculate the pipe length.

C) What is the wavelength and frequency of the 2nd harmonic?

Resonance

Resonance occurs when a vibration from

one oscillator occurs at a natural

frequency for another oscillator.

The first oscillator will cause the second to

vibrate.

Demonstration.

Beats

“Beats is the word physicists use to

describe the characteristic loud-soft

pattern that characterizes two nearly (but

not exactly) matched frequencies.

Musicians call this “being out of tune”.

Let’s hear (and see) a demo of this

phenomenon.

What word best describes this to

physicists?

Amplitude

Answer: beats

What word best describes this to

musicians?

Amplitude

Answer: bad intonation (being out of tune)