Waves A disturbance in a medium that transfers energy and momentum.
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Waves
A disturbance in a medium that transfers energy and momentum
To produce a Wave:
• A vibration (disturbance)
• A medium – a substance to travel through.
Examples of Waves
• Sound
• Light
• Water
There are two types of waves
Transverse – the individual wave particles move perpendicular to the velocity of the wave.
Examples:
Electromagnetic waves (light waves, radio waves, microwaves, x-rays)
Wave on a string
Longitudinal – the individual wave particles move parallel to the velocity of the wave.
Examples: Sound Waves
Parts of a wave:
Amplitude
Wavelength
Frequency – The number of wave cycles in 1 second.
Tf
1 Units 1/s = Hertz (Hz)
Wave Interference – The combination of two or more waves.
• Constructive interference – Two waves combine to make a bigger wave.
• Destructive interference – Two waves combine to make a smaller wave.
vTf
T1
fv1
wav
elen
gth
(m)
Period (s)
velocity
wavelength = (velocity)(Period)
fv
wav
elen
gth
(m)
frequency (hz)
The Wave Equation
fv v = velocity of the wave (m/s)
λ = wavelength (m)
f = frequency (1/s = Hz)
Example1: A sound wave has a frequency of 256 Hz. What is the wavelength? The speed of sound is 340m/s.
m
s
sm
f
v
fv
33.11
256
340
Example 2: A radio wave has a frequency of 96.9MHz. What is the wavelength? The speed of light is 3.0 x 108 m/s.
m
s
sm
f
v
fv
1.31
109.96
103
6
8
Standing Waves on a String
The velocity of a wave on the string depends on the mass per length of the string and the tension in the string.
LmF
v Tv = velocity of the wave (m/s)
FT= Tension in the string (N)
m = mass of the string (kg)
L = length of the string (m)
The fundamental frequency 1st Harmonic.
L2
v
f
fv
L
vf
21
L
The fundamental frequency 2nd Harmonic.
L
v
f
fv
L
vf 2
L
The fundamental frequency 3rd Harmonic.
L3
2
v
f
fv
L
vf
L
vf
2
332
3
3
L
The fundamental frequency 4th Harmonic.
2
L
v
f
fv
L
vf
Lv
f
22
4
4
L
The fundamental frequency 5th Harmonic.
L5
2
v
f
fv
L
vf
Lv
f
2
552
5
5
L
Summary
L
v
L
vf
L
v
l
vf
L
v
L
vf
L
v
L
vf
L
vf
2
5
25
2
24
2
3
23
22
2
5
4
3
2
1
fn=nf1
fn= nth harmonic
n = 1, 2 ,3, …..
f1 =1st harmonic (fundamental frequency)
Conditions for interference
L2
L1
P
δ = path difference = L2 – L1
Constructive Interference
δ = 0, λ, 2λ, 3λ …….
δ = nλ n = 0, 1, 2, 3, …
Destructive Interference
δ = λ/2, 3λ/2, 5λ/2 …….
δ = (n+ ½)λ
n = 0, 1, 2, 3, ….…
Sound Waves
• The speed of sound in air at room temperature is 340m/s.
• The speed of sound increases with increasing temperature.
• The speed of sound in water is 1500m/s.
• The speed of sound in aluminum is 5100m/s.
Physics Human
Perception
frequency
Intensity/Amplitude loudness
Pitch
Pressure fluctuations in air due to a vibrating tuning fork.
Applet
Frequency range of the human ear.
Ultra Sound
Human Ear
Sound intensity and the decibel scale
Beats
• Beats occur when two sound waves have slightly different frequencies interfere with one another.
• The number of beats per second is called the beat frequency.
• The beat frequency is determined by subtracting the two frequencies.
Standing Sound Waves in a Tube
• The wave travels at the speed of sound (340m/s)
• Open ends must have an antinode• Closed ends must have a node.• A pressure wave is set up in the tube.• A tube open at both ends acts just like the
string.• A tube closed at one end only has odd
harmonics.
Open Tube
3
23
LL21 L2
L
vf
L
vf
L
vf
2
3
2
3
2
1
Just like the string
Closed Tube
5
45
LL41
3
43
L
L
vf
L
vf
L
vf
4
54
34
5
3
1
Odd Harmonics
Resonance occurs when the driving frequency matches the natural frequency, resulting in large amplitude vibrations. Here are some examples of resonance
• Pushing someone on a swing.
• The Tacoma Narrows bridge.
• Breaking a wine glass with a sound wave
• Earthquakes totally destroying some buildings and not damaging others.
The Doppler Effect is a change in frequency (pitch) due to the relative motion of the sound source and observer.
• As the sound and listener approach each other the frequency is higher.
• As the sound and listener move away from each other the frequency is lower.
• The Doppler effect also occurs with light producing the red and green shift of distant stars.
• Doppler radar is used to track weather systems
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