What is sound ?
Mystery music of the day
You have 20 seconds to shout author
and title
Worth 1 (one) brownie point
Answer:
PHILIP GLASS, Rubric (from Glassworks,
1976)
Robert Boyle
1660
sound needs a medium to
propagate
sound is air in
motion, but it is
not wind
It’s an oscillation
Sound is a compression wave of matter
(usually air)
Energy propagates. Matter does not.
molecules in air
• are tiny, ~0.0000000003 m= 3 10-10 m across
• are fast moving, ~450 m/s ~ 1600 km/h ~ 1000 miles/h
~fast airplane
• are close to each other, ~ 0.000000003= 3 10-9 m = 10
molecule sizes
• fly about 0.0000001 m = 10-7m between collisions
• exert pressure
Pressure
force
on the
wall
Higher the temperature, density
higher the force
air
denser air
(more
molecules)
hotter air
(faster
molecules)
Pressure (P) is the force (F) per unit of area (A):
F = PA
The pressure on the air around us is enormous:
10 tons/m2 or 15 pounds/inch2
It doesn’t crush us because the pressure is also inside
us pushing out
We can now understand how sound propagates
compressed air
Mystery music of the day
You have 20 seconds to shout author
and title
Worth 1 (one) brownie point
World destruction, Afrika Bambaataa &
Johnny Lydon (1984)
Sound speed in gases is given by :
P
v

T
C
m
temperature
at constant entropy
(for scientists only)
(for everybody)
molecule mass
• heavier molecules are harder to push around,
sounds propagates slowly
• hotter air, faster molecules, faster sound
Our ears can detect tiny variations in air pressure:
• normal air pressure 100.000 Pa
• pressure variation for the just audible sound = 0.00002 Pa
• pressure variation on the pain threshold = 20 Pa
Sound exists also on liquids and solids
• Air (normal temperature) v = 344 m/s = 770
miles/hour or “5 seconds, one mile”
• Water v =1400 m/s
• Steel v = 5100 m/s
Properties of waves, sound include
Reflection
hard wall
If instead of a hard wall we have something more
flexible (but not elastic), much of the sound
energy will dissipate
acoustic insulator
Reflection on an angle
same angle
Someone at the red point can hear a conversation on the
blue point better than anybody else in the room
The same is said to occur in some gothic cathedrals
Band shell
Band shell
We hear a lot of reflected sound all the
time. It usually arrives very close to the
direct sound and we don’t notice it as a
distinct sound. Still, it contributes to the
quality of the sound.
Compare how an organ sounds in a
• cathedral
• outdoors
Compare how your voice sounds in a
• bathroom
• living room
We will discuss all this with more detail later…
Mystery music of the day
You have 20 seconds to shout author
and title
Worth 1 (one) brownie point
Answer:
DEBUSSY, Arabesque (1888)
Refraction
faster medium
slower medium
Initial and final directions are different.
The sound made a curve !
As an animation now
At night
During the day
colder air
hotter air
Acoustic lens
Diffraction
•Larger wavelength (~ obstacles) : more diffraction
•Shorter wavelength (<< obstacles) : less diffraction
“Inverse square law”: how sound intensity
decreases with distance
Intensity ~ 1/r2
It’s a good time now to read section 2.2 and
2.3 of Berg & Stork (except interference)
Mystery music of the day
You have 20 seconds to shout author
and title
Worth 1 (one) brownie point
Norwegian wood, Lennon & Mcartney (1966?)
How to read graphs
• figure what’s in the horizontal axis (w/ units)
• figure what’s in the vertical axis (w/ units)
• find the value of “savings” at any particular time
P  2xx
visual
analytical
2
WATCH !!!
same information
Let us watch now the graph of sound
pressure variation as a function of time for
some real sounds
• Which sounds are periodic ?
• What distinguishes noise from “musical” sounds ?
• What makes a sound louder ?
• What makes a sound lower or higher in pitch ?
Wavetools
http://www.physics.mcgill.ca/~grant/225B/Wavetoo
ls/Computerstuff.html
A very “pure” (but annoying) sound:
Mystery music of the day
You have 20 seconds to shout author
and title
Worth 1 (one) brownie point
Bachianas Brasileiras #5, Villa-Lobos (1938)
It is a good time now to read Berg & Stork,
Chapter 1
“Musical” sounds are periodic
amplitude (A)
period (T)
frequency (f) = 1/T, T=1/f
With a few qualifications …
amplitude = loudness
frequency = pitch
shape = timbre
• Period (T) = time for one cycle (measured in s, …)
• Frequency (f) = number of cycles per second
(measured in 1/s = Hz)
Example
T  2s 
1 1
1
f  
 0.5  0.5 Hz
T 2s
s
1
1
f  400 Hz  T  
 0.0025 s  2.5 ms
f 400 Hz
“Pure” tones are sine waves
Harmonic oscillator
P  A sin(2 f t )
amplitude
frequency
The mathematics of periodic waves
wavelength: distance between two crests
v
  vT 
f
period: time between two crests
T

v
frequency: how many crests per second
1 v
f 
T 
[Using a wave generator, find the lowest and
highest audible frequencies and calculate their
period and wavelength]
How sounds combine: adding two waves
Beats
Tartini tones
Interference movie
http://www.colorado.edu/physics/2000/schroedinger/
big_interference.html
It is a good time now to read Berg &
Stork,
Chapter 2.4, 2.5, 2.6, 2.7, 2.8, 2.9
Mystery music of the day
You have 20 seconds to shout author
(or performer) and title
Worth 1 (one) brownie point
All along the watchtower, Jimmy Hendrix
(1966)
http://www.loncapa.org/~mmp/applist/doppler/d.htm
Doppler effect
[go to the blackboard and do some real physics]
Applications:
• Doppler radar
• Doppler sonogram
• Expansion of the Universe
Ultrasound and sonograms
Typical frequencies: 300 MHz
1
f
  vT  v  340
m
1
0.000001 m
s 300.000.000 1
s