Waves and Sound
Waves and Sound
1 The Nature of Waves1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.
1 The Nature of Waves
Longitudinal Wave
1 The Nature of Waves
Transverse Wave
1 The Nature of Waves
Water waves are partially transverse and partially longitudinal.
2 Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and over again by the source.
In the figures, every segment of the slinky vibrates in simple harmonicmotion, provided the end of the slinky is moved in simple harmonicmotion.
2 Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is related to the period and has units of Hz, or s-1.
Tf
1
.2 Periodic Waves
f
Tv
.2 Periodic Waves
Example 1 The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric andmagnetic field disturbances traveling at a speed of 3.00x108m/s. A stationbroadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.
f
Tv
f
v
16.2 Periodic Waves
AM m 244Hz101230
sm1000.33
8
f
v
FM m 26.3Hz1091.9
sm1000.36
8
f
v
3 Wave Speed Versus Particle Speed on a String
Conceptual Example 3 Wave Speed Versus Particle Speed
Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?
4 The Nature of Sound WavesLONGITUDINAL SOUND WAVES
4 The Nature of Sound Waves
The distance between adjacent condensations is equal to the wavelength of the sound wave.
4 The Nature of Sound Waves
Individual air molecules are not carried along with the wave.
4 The Nature of Sound Waves
THE FREQUENCY OF A SOUND WAVE
The frequency is the number of cyclesper second.
A sound with a single frequency is calleda pure tone.
The brain interprets the frequency in termsof the subjective quality called pitch.
Check your Hearing
https://www.youtube.com/watch?v=qNf9nzvnd1k https://www.youtube.com/watch?v=VxcbppCX6Rk
4 The Nature of Sound Waves
THE PRESSURE AMPLITUDE OF A SOUND WAVE
Loudness is an attribute ofa sound that depends primarily on the pressure amplitudeof the wave.
4 The Speed of Sound
Sound travels through gases, liquids, and solids at considerablydifferent speeds.
4 The Speed of Sound
Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb
There is a rule of thumb for estimating how far away a thunderstorm is.After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives theapproximate distance (in miles) to the thunderstorm. Why does thisrule work?
4 The Speed of Sound
LIQUIDS SOLID BARS
adBv
Y
v
1. What is the wave speed if the period of a wave is 4 secondsand the wavelength is 1.8 m?
2 A fisherman noticed that a float makes 30 oscillations in 15seconds. The distance between to consecutive crests is 2 m.What is the wave speed?
3 What is the wavelength of a wave traveling with a speed of
6 m/s and a period of 3s?
4. What is the period of a wave traveling with a speed of 20 m/s and the wavelength is 4.0 m?
5. What is the wave speed if the period is 4.0 seconds and the wavelength is 1.8 m?
5 The Doppler Effect
The Doppler effect is the change in frequency or pitchof the sound detected byan observer because the soundsource and the observer havedifferent velocities with respectto the medium of sound propagation.
demohttp://www.animations.physics.unsw.edu.au/jw/doppler.htm#medium
visual effect:https://www.youtube.com/watch?v=h4OnBYrbCjY
Lewin demo:https://www.youtube.com/watch?v=wfcG0IRuffA
5 The Doppler Effect
A. MOVING SOURCE
Tvs
sssso fvfv
v
Tv
vvf
vv
ffs
so 1
1
5 The Doppler Effect
vv
ffs
so 1
1source movingtoward a stationaryobserver
source movingaway from a stationaryobserver
vv
ffs
so 1
1
5 The Doppler Effect
Example 10 The Sound of a Passing Train
A high-speed train is traveling at a speed of 44.7 m/s when the engineersounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a personstanding at the crossing, when the train is (a) approaching and (b) leavingthe crossing?
vv
ffs
so 1
1
vv
ffs
so 1
1
5 The Doppler Effect
Hz 4771
1Hz 415
sm343sm7.44
of
approaching
leaving
Hz 3671
1Hz 415
sm343sm7.44
of
5 The Doppler Effect
B. MOVING OBSERVER
v
vf
f
vf
vff
os
s
os
oso
1
1
5 The Doppler Effect
v
vff oso 1
v
vff oso 1
Observer movingtowards stationarysource
Observer movingaway from stationary source
16.9 The Doppler Effect
v
vv
v
ffs
o
so
1
1
GENERAL CASE
Numerator: plus sign applies when observer moves towards the source
Denominator: minus sign applies when source moves towards the observer
6. Standing wave
•Wave reflection at boundaries
•Principle of superposition, interference
•Standing waves on a string
•Normal modes
Reflection of a wave pulse at a boundary
Fixed end Free end
Pulse incident from right is reflected from the boundary at left
HOW the pulse is reflected depends on the boundary conditions
For fixed end, reflected pulse is inverted
For free (in transverse direction) end, reflected pulse is same way up.
time
Frictionless sliding ring Check using phet simulation
Reflection of a wave pulse at a boundaryBehaviour at interface can be modelled as sum of two pulses moving in opposite directions at the interface:
Transverse displacement always 0 at interface
“fixed end” “free end”
Transverse force
always 0 at interface
Standing WavesA standing wave is
produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave:
• Antinodes – Areas of MAXIMUM AMPLITUDE
• Nodes – Areas of ZERO AMPLITUDE.
Comparison between standing wave and travelling wave
Travelling wave
particles undergo SHM
all particles have same amplitude
all particles have same frequency,
adjacent particles have different phase
Standing wave
particles undergo SHM
adjacent particles have different amplitude
all particles have same frequency
all particles on same side of a node have same phase. Particles on opposite sides of
node are in antiphase
Some very basic physics of stringed instruments……….
The fundamental frequency determines the pitch of the note.
the higher harmonics determine the “colour” or “timbre” of the note.
(ie why different instruments sound different)
Fundamental wavelength = 2L
From v = fλ,
f1= v/2L
So, for a string of fixed length, the pitch is determined by the wave velocity on the string…..
Example Calculation
The string length on standard violin is 325mm. What tension is required to tune a steel “A” string (diameter =0.5mm) to correct pitch (f=440Hz)?
Density of steel = 8g cm
Sound WavesThe production of sound involves setting up a wave in air. To set up
a CONTINUOUS sound you will need to set a standing wave pattern.
Three LARGE CLASSES of instruments• Stringed - standing wave is set up in a tightly stretched string• Percussion - standing wave is produced by the vibration of solid
objects• Wind - standing wave is set up in a column of air that is either
OPEN or CLOSED
Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE
Closed PipesHave an antinode at one end and a node at the other. Each sound
you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound?
You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength.
This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.
Closed Pipes - HarmonicsHarmonics are
MULTIPLES of the fundamental frequency.
In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NOSOUND is produced
Closed Pipes - HarmonicsIn a closed pipe you have an ANTINODE at the 3rd
harmonic position, therefore SOUND is produced.
CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!
Open PipesOPEN PIPES- have an antinode on BOTH ends of the
tube. What is the SMALLEST length of pipe you can have to hear a sound?
You will get your FIRST sound when the length of the pipe equals one-half of awavelength.
Open Pipes - HarmonicsSince harmonics are MULTIPLES of the
fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH.
The picture above is the SECOND harmonic or the FIRST OVERTONE.
Open pipes - HarmonicsAnother half of a wavelength would ALSO produce an
antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends
The picture above is the THIRD harmonic or the SECOND OVERTONE.
CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!
ExampleThe speed of sound waves in air is found to be 340
m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm.
f
f
lfv
)675.0(2340
2
251.85 HZ
ExampleThe windpipe of a typical whooping crane is about
1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37°C.
f
fv
lfv
soundspeed
)525.1(4
4
331)]37)(6.0[( 353.2 m/s
57.90 Hz
Resonance demohttps://www.youtube.com/watch?v=1K5p9DfsXGo
Destructive:https://www.youtube.com/watch?v=j-zczJXSxnw
Sound wave energy on water:“Sound,Bass,Water, Sound makes water come alive with cymatics”
Wave with Bill Nyehttps://www.youtube.com/watch?v=YsKC_EtUHcA“Bill Nye The Science Guy & Waves & Full Episode”