waves and vibrations chapter 14 waves are all around us in everyday life
TRANSCRIPT
Waves and Vibrations
Chapter 14
Waves are all around us in everyday life.
Sound is a Wave.
Radio, TV, and Cell Phones use waves.
Light is a wave.*
*But it can act as a particle…another story in Physics!
Main concepts
• Types of waves: – Transverse: waves on strings– Longitudinal: sound waves – water waves are more complex (combination)
• Relationship of wavelength, frequency and velocity of wave (f=v)
• Wave amplitudes can be added together.• Addition of waves leads to interference:
constructive or destructive
Motion of a Transverse Wave on a string
• Wave amplitude is y=Asin[2(x/ - ft)]
• If you sit at one location x, the wave oscillates in time.
• If you stop the action at a time t, the wave oscillates as a function of distance x.
The wave crest travels a distance in one period of time, 1/f. Thus the speed is the distance over the time, or
f=v
Motion of Longitudinal Wave
• Pressure wave• Oscillation of local pressure and gas density
Wavelength
Water waves combine motions
Complex motion: combination of transverse and longitudinal motion.
Light & Radio are Electro-magnetic Waves
Electric Field (and Magnetic Field) move TRANSVERSE to direction of propagation of energy.
++++++
------
Ant
enna
Key characteristic of these waves
• Energy (in the form of motion) can be transmitted by the wave
• The medium (the string, the air, the water) does not move at the speed of the wave—it essentially “stays put”
• The energy of the wave is transmitted through the medium from one piece of matter to another
• Note that light waves travel without the need for a medium at all!
Demonstrations
• Transverse waves (long spring)
• Transverse waves (tuning fork)
• Transverse waves (wave machine)
• Longitudinal wave/transverse wave (metal rod)
• Longitudinal wave (open tube)
• Longitudinal wave (recorder)
Superposition (addition) of waves
Wave amplitudes are added. They can get larger (constructive) or smaller (destructive) interference when they are superposed.
Wave interference
CONSTRUCTIVE DESTRUCTIVE
Demonstrations: waves on a rope.
• Reflection of wave at rigid wall
• Destructive interference
• Standing waves
Physlets Illustration 17.3 superposition of pulsesIllustration 17.4 superposition to make a standing wave.Exploration 17.4 superposition of two cosine waves to make a standing wave.
Addition of 2 waves that are close in frequency
Beat Frequency
Demonstration
• Beat frequency with tuning forks
Standing waves on strings
=2L f
=L 2f
First harmonic
Second harmonic
=2/3 L 3f Third harmonic
(one octave)
Standing waves in columns of air
4L 4/3 L 4/5L2L L 2/3L
Closed vs. open pipes.The closed pipe has a lower fundamental frequency.The closed pipe has only “odd” harmonics. The open pipe has odd and even.
An “octave” is a doubling of the frequency of a note. Our theory predicts a tube will produce a note one octave lower if it is closed off on one end. Try it!
A “harmonic” is a multiple of the fundamental frequency, f, 2f, 3f, etc.
f 3f 5f f 2f 3f
Intensity of Sound• Our perception of sound is that a sound with 10
times the intensity sounds TWICE as loud• To make it easier to compare sound levels, we
use the “decibel (dB)” scale
0
log10I
I
“Beta” is the “intensity LEVEL”. I is the “intensity”. Be careful. Intensity level (dB) is dimensionless. Intensity has units of power/area.
Various sound intensitiesLoudest sound produced in laboratory 109
Saturn V rocket at 50 m 108
Rupture of the eardrum 104
Jet engine at 50 m 10
Threshold of pain 1
Rock concert 10–1
Jackhammer at 1 m 10–3
Heavy street traffic 10–5
Conversation at 1 m 10–6
Classroom 10–7
Whisper at 1 m 10–10
Normal breathing 10–11
Threshold of hearing 10–12
120dB
0dB
50dB
20dB
110dB
dB scale of loudness
THESE ARE THE SAME:
1. Increase in sound intensity (P/A) of an order of magnitude.
2. Increase in intensity level (dB) of 10 units.
3. Double the “loudness”.
Intensity vs. distance from a point source
Sound is created at origin with power P.It gets spread over the area of an entire sphere of radius R.The sphere area is A=4r2.
Therefore, the Intensity, P/A, falls off like 1/r2.
R1
R2
P
Comparing sound levels
• The decibel (dB) is often used to compare sounds.
• The reference intensity, I0, is the weakest sound that can be heard.
Example:
A person talking has a sound level of about 50 dB. What is the sound level of 100 people talking?
dBI
I50log10
0
11
dB
I
I
I
I
70
log10100log10
*100log10
0
1
0
1100
The intensity level increases 10 dB for every 10 time increase in intensity.
Fix the noise!
• A factory has 50 machines that produce a total of 100 dB of noise. The Federal standard is that the total must be less than 90 dB.
• How many machines can you operate legally at one time?
You must reduce the total noise intensity level by 10 dB. This means a reduction in noise intensity of a factor of 10.
A: You must reduce the number of machines by 10, to 5!
Looked at another way….
Adding sound levels• Given that 50 machines produce a dB
level of 100, what is the dB level of one machine?
1
0
1
0
150
0.17
log1050log10
100*50
log10
dB
I
I
dBI
I
dB
dBdB
83
0.171001
Intensity and distance• You are standing 1
meter from a model rocket which takes off producing a sound level of about 85 dB. What is the sound level 100 meters away?
A: Using the 1/r2 law, the Intensity of the sound (P/A) 100 meters away is 104 times less. This means the sound level is reduced by 40 dB. The sound level is 45 dB at 100 meters.