waves and sound - mr. peppard's physics...
TRANSCRIPT
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)