PHY2464 - The Physical Basis of Music
PHY
-2464
PHY-2464
Physical Basis of Music
Presentation
Presentation 33
Basics
Basics of
of Sound
Sound Waves
Waves –– Part
Part B
B
An
An edited
edited version
version of
of Sam
Sam Matteson’s
Matteson’s Unit
Unit 11 Session
Session 33
Sam
Sam Trickey
Trickey
January
10-12,
January 10-12, 2005
2005
PHYPHY-2464
Pres. 3 Sound Waves - B
Quick Quiz:
If a person can only distinguish an echo if it
occurs more than 0.100 sec after the initial
sound, how far from a wall must s/he be to
hear a distinct echo of clapping hands?
Round trip time = 0.1 sec.
One way = (0.1)/2 sec= 0.05 sec
d = v x t = (343 m/s)x(0.05 sec) = 17.1 m ≈57 feet
1
PHY2464 - The Physical Basis of Music
PHY-2464 Pres. 3 Sound Waves - B
Pressure and Force: intertwined in everyday life,
but not in Physics.
Force: push, pull, tug, etc. that causes an object
to be accelerated.
Acceleration: change in velocity
Isaac Newton: [1] No net force → constant
velocity
[2] Ftotal = m • a
[3] I push on you ↔ you push on me
PHY-2464 Pres. 3 Sound Waves - B
Units of Force: 1 Newton = 1 kg x 1 m/s2
On earth: 1 kg weighs 9.8 N = 2.2 pounds
→ 4.45 Newton per pound
2
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Pressure = Force per unit Area
p = F /A
Force applied perpendicular to Area
PHYPHY-2464
Pres. 3 Sound Waves - B
Fact - The metric (SI) unit of pressure is the
Pascal [Pa] = 1 Newton/ m2
Pressure = 1 Pascal:
1 Newton force
1 square meter area
3
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Fact – “Standard atmosphere”
= 1.0 atm
=101 kPa
=14.7 pound / square inch
Tire pressure =A few 100 kPa
(Over atmospheric = “gauge
pressure”)
PHYPHY-2464
Pres. 3 Sound Waves - B
Which applies the
greatest pressure on
the ground?
4
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Force = 200 lb = 891 N
Foot Area = 36.2 in2 = 0.023 m2
p = F/A =200/(2 x 36.2) = 2.8 psi
p = 891/(2 x 0.023) = 19 kPa
Force = 4,000 lb = 17,800 N
Foot Area = 43.5 in2 = 0.028 m2
p = F/A =4000/(4 x 43.5) = 23. psi
p = 17800/(4 x 0.028) = 159 kPa
Force = 100 lb = 445 N
Foot Area = 12.7 in2 = .0082 m2
p = F/A =100/(2 x 12.7) = 3.9 psi
p = 445/(2 x 0.0082) = 27 kPa
PHYPHY-2464
Pres. 3 Sound Waves - B
p = 19 kPa
p = 159 kPa
p = 27 kPa
Force = 100 lb = 445 N
Heel Area = 0.16 in2 = .0001 m2
p = F/A =100/(2 x 0.16) = 313. psi
p = 445/(2 x 0.0001) = 2200. kPa
5
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Bed of Nails:
Pressure is NOT Force
PHYPHY-2464
Pres. 3 Sound Waves - B
Recall Fact: Pressure = Force per unit Area
p = F /A
Same Force
Different Area
∴Different Pressure
6
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Sound is a pressure wave.
PHYPHY-2464
Pres. 3 Sound Waves - B
Talking About Periodic Waves
7
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Frequency f is the number of cycles or
pulses per unit time.
[ f ] = Hertz = Hz = 1/sec
PHYPHY-2464
Pres. 3 Sound Waves - B
Period is the time it takes to make one cycle,
oscillation or pulse.
[P] = second
Fact (deduced) P = 1/ f
8
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Wavelength λ is the distance from one point
on a wave to a corresponding point (the
point of “same phase”) on the next cycle.
[λ]= m
λ
λ
PHYPHY-2464
λ
Pres. 3 Sound Waves - B
Wavelength
⃒⃖
V⃗⃗⃗
λ
⃒⃗
⃗⃖
⃖⃗
9
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Chain of Inference:
1. The distance a wave moves in one cycle = λ
2. Time for one cycle = period P
3. v = distance moved / time to move
4. →
PHYPHY-2464
v=λ/P=λ⋅f
Pres. 3 Sound Waves - B
Fact:
v=λ⋅f
Always!
10
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Fact:
Sound travels faster in warm air than in cold.
PHYPHY-2464
Pres. 3 Sound Waves - B
Most accurate relationship of sound velocity on
temperature (in Kelvin) is
v = 343 √{(T +293)/293} m/s
11
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Fact: Common, convenient approximation of
the relationship of sound velocity and
temperature (in CELSIUS)
v = 331 +0.6T m/s
What is the speed of sound on a hot day when it is 40 C?
v = 331 + 0.6 (40) = 331 + 24 = 355 m/s
PHYPHY-2464
Pres. 3 Sound Waves - B
Velocity of Sound vs Temperature
Velocity of Sound
(m/s)
700
600
500
400
300
200
Exact formula
Approximate formula
100
0
-300
-200
-100
0
100
200
300
400
500
600
Temperature (C)
12
PHY2464 - The Physical Basis of Music
PHYPHY-2464
Pres. 3 Sound Waves - B
Summary:
•
•
•
•
•
•
•
p=F/A
Standard atmospheric pressure = 101 kPa
Frequency = number of cycles per second
Hz = Hertz = cycle/second
Period P = 1/ f
v=λ⋅f
v = 343 + 0.6 T m/s [T in Celsius]
PHYPHY-2464
Pres. 3 Sound Waves - B
Credits:
•
Photographs & Graphics
•
Ross Clarke-Jones from www.??
13