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PHY II – Waves
The Wave Model Speed of Waves on a String Sinusoidal Waves Spherical Waves, Plane Waves
Transverse versus Longitudinal
Snapshot Graph
History Graph
A string of beads are connected by a set of tiny springs. At the instant the clock starts (t=0), a pulse is moving to the right on the beads and the snapshot graph looks like this:
Which of the following history graphs tracks the position for the bead marked with a red arrow as a function of time?
The graph at the top is the history graph at x = 4 m of a wave traveling to the right at a speed of 2 m/s. Which is the history graph of this wave at x = 0 m?
(A) (B) (C)
Sinusoidal Waves
What is the frequency of this traveling wave?
A. 10 Hz
B. 5 Hz
C. 2 Hz
D. 0.2 Hz
E. 0.1 Hz
Quiz 2
What is the phase difference between the maximum of a wave and the adjacent minimum? (crest to trough)
A. 0
B. π /4
C. π /2
D. 3 π /2
E. π
Quiz 3
Sinusoidal Wave Snapshot Graph
k = 2π/λ is the wave number
Sinusoidal Wave History Graph
ω=2π/T is the angular frequency
PHY II – Waves
• Sound and Light
• Medical Applications of Ultrasound
• Power and Intensity
• The Doppler Effect
Sound and Light• Sound is a pressure wave in a gas, liquid
or solid. Speed depends on material.
• Light is one type of electromagnetic wave.
• In a vacuum, all electromagnetic waves (including light) travel at c = 3×108 m/s.
• In transparent media, light slows down. Index of Refraction is n > 1.
• This reduces the wavelength, but does not change the frequency!
A light wave travels through three transparent materials of equal thickness. Rank is order, from the largest to smallest, the indices of refraction n1, n2, and n3.
A. n2 > n1 > n3 B. n3 > n1 > n2 C. n1 > n2 > n3
D. n3 > n2 > n1 E. n1 = n2 = n3
Reflection of Transverse Wave Pulse
• A pulse traveling to the right on a heavy string attached to a lighter string
• Speed suddenly increases
Reflection of Transverse Wave Pulse
• A pulse traveling to the right on a light string attached to a heavier string
• Speed suddenly decreases
Physics of Ultrasound• Speed of sound in bone, flesh and
blood are all different• When the speed of any wave suddenly
changes, there is a reflection and transmission
• Ultrasound images are formed from reflected high frequency sound
• Image resolution is set by wavelength, λ• λ=v/f, so higher frequency yields smaller λ, and better resolution
Speed of sound in humansTissue Sound Speed (m/s)
Air 350
Fat 1450
Brain 1540
Blood 1570
Bone 4080
Muscle 1585
Power and Intensity• The Power, P, of any wave source is how
much energy per second is radiated as waves [units = Watts]
• The Intensity, I, is the energy rate per area. This determines how loud (sound) or bright (light) the wave is.
• I=P/a, where a is an area perpendicular to the wave direction.
• At a distance r from a spherically symmetric source, the intensity is I=P/(4πr2)
Chapter 20, Problem 34• The sound intensity from a jack hammer
breaking concrete is 2 W/m2 at a distance of 2 m from the point of impact. This is sufficiently loud to cause permanent hearing damage if the operator doesn’t wear ear protection. What is the sound intensity for a person watching from 50 m away?
Doppler Effect
Valerie is standing in the middle of the road, as a police car approaches her at a constant speed, v. The siren on the police car emits a “rest frequency” of f0.
Which statement is true?
A. The frequency she hears rises steadily as the police car gets closer and closer.
B. The frequency she hears steadily decreases as the police car gets closer and closer.
C.The frequency she hears does not change as the police car gets closer.
Valerie is standing still as a police car approaches her at a constant speed, v. Daniel is in his car moving at the same constant speed, v, toward an identical police car which is standing still. Both hear a siren.
Which statement is true?
A. The frequency Daniel hears is lower than the frequency Valerie hears.
B. The frequency Daniel hears is higher than the frequency Valerie hears.
C.The frequencies that Daniel and Valerie hear are exactly the same.
(Almost correct)
Actual Answer! Check eq.20.38
and 20.39!
PHY II – Waves
• The Principle of Superposition• Standing Waves• The Guitar: Stringed
Instruments• The Trumpet: Wind Instruments
Principle of Superposition• If two or more waves combine at a
given point, the resulting disturbance is the sum of the disturbances of the individual waves.
• Two traveling waves can pass through each other without being destroyed or even altered!
Some Results of Superposition:• Two waves, same wavelength and
frequency, opposite direction:
Standing Wave
• Two waves, same wavelength and frequency, similar direction, different phase:
Interference
• Two waves, same direction, slightly different frequency and wavelength:
Beats!
Standing Wave:The superposition of two 1-D sinusoidal waves traveling in opposite directions.
Standing Waves• Are a form of “resonance”• There are multiple resonant frequencies
called harmonics• The boundary conditions and speed of
waves determine which frequencies are allowed.
• The ends of the resonant cavity have forced nodes or antinodes
• With a wave on a string, it is possible to force an intermediate node
OMGWTFBBQOMGWTFBBQStanding Wave in PressureStanding Wave in Pressure
Forces the Flames higher at Forces the Flames higher at antinodesantinodes!!
Harmonic frequenciesTransverse standing wave on a string
clamped at both ends: there are nodes in displacement at both ends.
,...)3,2,1(2
mL
vmfm
Standing sound wave in a tube open at both ends: there are nodes in pressure both ends.
,...)3,2,1(2
mL
vmfm
Harmonic frequenciesStanding sound wave in a tube closed at one end: there is a node in pressure at the open end, and an anti-node at the closed end.
,...)5,3,1(4
mL
vmfm
PHY II – Waves
•Constructive and Destructive Interference
•Interference Patterns•Beats
Wave Interference• Two waves moving in the same direction
with the same amplitude and same frequency form a new wave with amplitude:
2
cos2
aA
where a is the amplitude of either of the individual waves, and is their phase difference.
Beat frequency• Beats are loud sounds separated by soft sounds• The beat frequency is the difference of the
frequencies of the two waves that are being added:
21mod2 ffffbeat • The frequency of the actual sound is the
average of the frequencies of the two waves that are being added:
221 ff
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