Download - Chapter 6
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CHAPTER OUTLINE
Wave Concept Wave Properties Wave Speed Wave Types Electromagnetic
Waves
Sound Waves Speed of Sound Doppler Effect Standing Waves Resonance
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CONCEPT OF WAVES
A wave is a disturbance that propagates through a system transferring energy
Waves transfer E!
(courtesy of Dr. Dan Russell, Kettering Univ.)
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WAVE PROPERTIES
Crest: the highest point on a wave
Trough: the lowest point on a wave
Amplitude: maximum displacement in a wave
height of crest or depth of trough
Amplitude is related to the E
of a wave
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WAVE PROPERTIES
Wavelength (λ): distance between 2 successive crests
Frequency (f): # of waves produced per unit time.
Units = m or cm
Units = 1/s = Hz
Period (T): # of seconds per unit wave.
1f =
T
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WAVE SPEED
The speed of a wave can be calculated from its frequency (f) and wavelength (λ).
f × λ = s
Units:
Note, s = constantfor a given wave
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Example 1:
A sound wave has a speed of 344 m/s and a wave-length of 0.5 m. What is the frequency of this wave?
f = ???
λ = 0.5 m
s = 344 m/sf = 688 Hz
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Example 2:
sλ =
f
344 m/s=
20 x 1000 Hzf = 20 kHz
λ = ???
s = 344 m/s λ = 0.017 m
A sound wave has a speed of 344 m/s has a frequency of 20 kHz. What is this wave’s wavelength?
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Example 3:
An ocean wave passes a point on the pier at the rate of 12 waves per minute. What are the frequency and period of this wave?
# of cycles = 12
time = 60 s
f = ???
T = ???
f = 0.2 Hz
T = 5 s
12 waves=
60 s
1=
0.2 Hz
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LONGITUDINALWAVES
Waves where direction of particle movement is parallel to the direction of wave velocity, are longitudinal waves
Longitudinal waves have areas of high particle density (compressions) and of low particle density (rarefactions)
Sound is the most common example of a longitudinal wave.
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TRANSVERSEWAVES
Waves where the direction of particle movement is perpendicular to the direction of wave velocity, are transverse waves
i.e. mechanical waves, electromagnetic waves (light, microwave, x-rays, etc.)
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ELECTROMAGNETICWAVES
Electromagnetic waves (e&m waves) are transverse waves caused by vibrating electrons (e-) Formed through interaction of electric and magnetic fields that
are perpendicular to one another
In vacuum, e&m waves travel at the same speed and differ from each other only in freq.
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ELECTROMAGNETICSPECTRUM
The classification of electromagnetic waves according to their frequency is called electro-magnetic spectrum.
e&m waves range from γ rays (short λ , high f) to radio (long λ, low f)
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SOUND WAVES
Sound is the most common example of a longitudinal wave
In sound waves, the molecules of air transmit the vibrations through compressions and rarefactions
Sounds waves cannot travel in vacuum!
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SPEED OF SOUND
Speed of sound is affected by: wind conditions, temperature, humidity and type of medium NOT affected by its loundness (amplitude)
Sound travels faster in liquids and solids compared to gases Closely packed molecules in solids and liquids will transmit the
vibrations faster than in gases
Sound travels faster at higher T Faster moving air particles bump into each other more
frequently and carry vibrations in shorter time
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DOPPLER EFFECT
The apparent shift in pitch of sound when the source is moving relative to the observer is called the Doppler Effect
i.e. The sudden change in pitch of an ambulance siren as it goes by an observer is the result of the Doppler effect
Pitch of a sound is the subjective measure of its frequency High frequency sounds have high pitch, and low frequency sounds
have low pitch
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STANDING WAVES
Waves that are reflected on themselves and appear to “stand” are called standing waves
Standing waves produce the variety of sounds in musical instruments! (Animation) violin
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RESONANCE
Every object has natural vibrations caused by motion of its molecules
When a forced vibration matches an object’s natural vibrations, a dramatic increase in amplitude occurs This phenomena is called Resonance
Some Examples Tacoma Narrows Bridge Resonant Bridge
Some Symbols Used
• all• there is or there exists• Change• infinity• multiplication• proportional to• less than or equal to• greater than or equal to• plus or minus• degrees• therefore• ≈ approximately equal to• decreases• increases
• λ – Wavelength• E – Energy• H – Heat• # - Number• e- - electron• p+ - proton