Test 4 Sound

1
Test 4 Sound WavesReview

• PHYS 2326-30

2
Test Results

• Average Grade was 65
• A 8
• B 4
• C 5
• D 7
• F 9

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Current Course Results

• Average 70.5
• A 7
• B 4
• C 9
• D 7
• F - 12

4

• 1. An automobile having a mass of 1,000 kg is
  driven into a brick wall. The cars bumper
  behaves like a spring of constant 5.00 E 6 N/m
  and compresses 3.16cm as the car is brought to
  rest.
• a) If a wrecker picks the car up off the ground
  by the bumper, at what frequency will it
  oscillate?
• b) What was the speed of the car before impact,
  assuming no energy loss during the impact?

5

• Simple harmonic motion problem based on problem
  15-15

6

• 2. A sinusoidal wave is traveling along a rope.
  An oscillator on one end is generating this wave
  and completes 40 vibrations in 30.0 seconds. A
  maximum travels 425 cm along the rope in 2.0
  seconds.
• a) What is the wavelength of the wave?
• b) If the mass of the rope is 1kg and it is 10m
  long, what is the tension on the rope?

7

• 40vibs/30sec 1.33 vibs/sec 1.33 Hz
• 425cm/2.0 sec 4.25m/2.0sec 2.125m/s
• µ 1kg/10m 0.1 kg/m
• vf?, ?v/f 2.125/1.33 1.59 m
• v sqrt(T/µ), T tension, µmass/length
• v2 T/ µ , T µ v2 (0.1) (2.125)2 0.45 N

8

• 3. Calculate the sound level in dB of a sound
  wave that has an intensity of 4.00 microwatts/m2
• Io 1.0 x 10-12 W/m2
• dB 10 log(I/Io) (10) log (4.0x10-6/ 1.0 x
  10-12 ) (10)(6.6) 66 dB

9

• 4. A 384Hz tuning fork is placed over the top of
  an open pipe, closed on the bottom by a piston.
  Starting at the top, the piston is drawn down and
  resonances are heard when the piston is 22.8cm
  from the top and when the piston is 68.3 cm below
  the top. What is the velocity of air implied by
  this experiment?
• Resonances are occurring at antinodes which are ½
  ? intervals (68.3 22.8) 45.5 cm, ?2
  (45.5cm) 0.91m
• vf ? (384)(0.91) 349.44 m/s

10

• 5. A skater skating towards a wall at 4m/s blows
  a whistle with an 800Hz tone when 100 meters from
  the wall. Assume the speed of sound is 345m/s
• a) What frequency is heard by someone standing by
  the wall?
• b) What frequency is heard by the skater from the
  reflected sound?
• c) What is the beat frequency heard by the
  skater?
• d) As the skater gets closer to the wall and the
  reflected sound gets louder, what is the
  resulting tone heard by the skater?

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• a) f (vvo)/(v-vs)f (3450)/(345-4)(800)
  809.4 Hz
• b) f (vvo)/(v-vs)f (3454)/(345-0)(809.4)
  818.76 Hz
• c) Beat Frequency heard by skater
• fb f f 818.76 800 18.76 Hz
• d) Skater hears the average of the two
  frequencies (ff)/2 809.4 Hz

12

• Given a wave equation, y 0.2 sin(2t 3x), find
  
• Amplitude?
• Wavelength?
• Frequency?
• Period?
• Velocity?

13

• wave eqn given fits the general form
• y A sin(?t kx), wave traveling in x
  direction
• Amplitude 0.2m
• Wavelength K 3 2p/?, ? 2 p/k
• 2/3 p meters 2.09 m
• c) Frequency ? 2 2 p f, f ?/(2 p) 2/(2
  p) 0.318 Hz
• d) Period 1/f 1/0.318 3.14 seconds
• e) velocity ?/k 2/3 0.66 m/s

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• Bonus Question
• At what temperature is the speed of sound in air
  equal to 345m/s assuming air is an ideal gas with
  a molecular mass of 28.8 E-3 kg/mole and that air
  is diatomic with gamma 1.4. The gas constant
  is 8.315 J/mol.K

15
Chapter 35 Light
PHYS 2326-30
16
Concepts to Know

• Speed of Light
• Wave Fronts Rays
• Reflection
• Law of Reflection
• Refraction
• Index of Refraction
• Law of Refraction (Snells Law)
• Total Internal Reflection

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Concepts to Know

• Critical Angle
• Huygens Principle
• Dispersion

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Light

• In some cases exhibits particle behavior
• x-rays
• gamma rays
• In other cases exhibits wave properties
• visible light
• radio waves
• Its all the same stuff

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Speed of Light

• Light is very fast
• 2.998 x 10 8 m/s in a vacuum (3.0E8 )
• slower in materials such as air or glass

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Rays

• Can assume light travels in fixed directions in a
  straight line when passing through a uniform
  medium
• This is the ray approximation
• Rays are perpendicular to wavefronts
• Works well for studying mirrors, lenses, prisms
  and optical instruments like telescopes
• Light ray paths are reversible

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Reflection

• Like waves traveling along a string hitting a
  boundary, light can reflect when hitting a
  boundary
• Unlike a string, light doesnt have to reflect
  back along the same direction
• Specular reflection is from a smooth surface like
  a mirror or a calm pond
• Diffuse reflection occurs from rough surfaces

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Law of Reflection

• Given a smooth surface at a point, there is a
  normal to that surface
• Reflection occurs so that the angle of the
  reflected ray is the same as the angle of the
  incoming or incident ray both measured from the
  normal

?
?
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Refraction

• When a boundary exists between two different
  transparent media, the light ray passing through
  the boundary is bent and is said to be refracted,
  depending upon the properties of the two media
• The relationship for this is eqn 35.3
• where ?1 and v 1 are the angle of incidence and
  speed of light in the first medium and ?2 and v2
  are for the second medium

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Refraction Reflection

• Usually, both occur at a boundary
• When going from air to a denser material with a
  lower speed of light water, glass refraction
  bends the ray towards the normal
• When going from denser material to air, the ray
  bends away from the normal

N
?1
?1
?2
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• Example of light going through a glass to air
• As light travels from one medium to another, the
  frequency doesnt change but the wavelength and
  velocity change

?2
N
?1
?1
?1
?2
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Index of Refraction

• n defined as c/v the ratio of the speed of
  light in a vacuum divided by the speed of light
  in the medium

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Refractive Index

• Table 35.1 shows a refractive index for various
  materials
• A vacuum is 1.00000000
• Air is close at 1.000293
• Water is just over 1.3
• Glass varies around 1.4 to 1.7

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Huygenss Principle

• All points on a given wave are taken as point
  sources for the production of spherical secondary
  waves called wavelets

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Dispersion

• The index of refraction is not constant with
  wavelength
• Dispersion is the behavoir where the angle of
  refraction changes with wavelength
• This creates the rainbow effect of rain droplets
  and prisms

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Total Internal Reflection

• Note that a sin function varies from -1 to 1 and
  that the typical index of refraction n can vary
  from 1.0 to over 2.0.
• For a surface boundary between materials 1 and 2,
  where material 1 has a greater index of
  refraction than material 2, what happens when the
  angle ?2 reaches 90 degrees?

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• n1 sin ?1 n2 sin 90 n2
• ?1 becomes the critical angle ?c
• sin ?1 n2 / n1 (for n1 gt n2) eqn 35.10
• As the incident angle ?1 reaches the critical
  angle ?c there is total internal reflection going
  on as all light is reflected since the refraction
  angle cannot exceed 90.

gt?c