Sound Test

1
Sound Test

• Answers

2
Question 1

• What is the frequency of the pendulum given the
  graph of its horizontal position as a function of
  time? Show your work.
• Frequency 1 cycle .333 Hz
• 3 seconds

3
Question 2

• What is the period of the pendulum given the
  graph of its horizontal position as a function of
  time? Show your work or explain your reasoning.
• Period the time it takes to complete 1 cycle.
• It took 3 seconds for this pendulum to complete 1
  cycle.

4
Question 3

• What is the length of this pendulum if the
  acceleration due to gravity is 9.8 m/s2?
• Tp 2p L
• 
  g

5
Question 3

• What is the length of this pendulum if the
  acceleration due to gravity is 9.8 m/s2?
• Tp2 (2p)2 L
• 
  g

6
Question 3

• What is the length of this pendulum if the
  acceleration due to gravity is 9.8 m/s2?
• Tp2 g L
• (2p)2
• (3.0s)2 9.8 m/s2 L 2.2 m
• (2p)2

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Question 4

• a) What would happen to the period and the
  frequency of oscillation if the acceleration due
  to gravity changed to 19.6 m/s2? Explain your
  reasoning.

8
Question 4

• What would happen to the period and the frequency
  of oscillation if the acceleration due to gravity
  changed to 19.6 m/s2? Explain your reasoning.
• Tp 2p L
• 
  g

9
Question 4

• Since the period (Tp) is inversely related to the
  square root of the acceleration due to gravity
  (g) the period will decrease with an increase in
  acceleration. The frequency will increase because
  T 1/f
• Tp 2p L
• 
  g

10
Question 4

• b) What would happen to the frequency if the if
  the mass of the pendulum bob were
• quadrupled?
• The period of a pendulum is independent of the
  mass of the pendulum and therefore will remain
  the same.

11
Question 5

• The amplitude of the mass on the string would be
  1.0 m up to the peak
• Or
• The amplitude of the mass on the spring would be
  1.0 m down to the trough

12
Question 6

• What would happen to the period and frequency of
  oscillation for this mass spring system if the
  acceleration due to gravity changed to 19.6 m/s2?
  Explain your reasoning.
• The period and frequency of a mass attached to a
  spring are independent of the acceleration due to
  gravity therefore the period and frequency remain
  the same

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Question 6

• What would happen to the frequency if the mass
  were quadrupled? Explain your reasoning.

14
Question 6

• What would happen to the frequency if the mass
  were quadrupled? Explain your reasoning.
• Ts 2p m
• K

15
Question 6

• The period would increase by the square root
  of 4 or double. The frequency would decrease by
  the square root of 4 or decrease by 1/2
• Ts 2p m
• K

16
Question 7

• What is the period of oscillation of a 1.0 kg
  mass attached to a 50.0 N / m spring that has
  been displaced 5.0 cm from its equilibrium
  position?
• Ts 2p m
• K

17
Question 7

• What is the period of oscillation of a 1.0 kg
  mass attached to a 50.0 N / m spring that has
  been displaced 5.0 cm from its equilibrium
  position?
• .89 s Ts 2p 1.0 kg
• 
  50 N / m

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Question 8

• a) A guitar string has linear density of .020 kg
  / m. The tension on the guitar string is 20.0 N
  what is the velocity of a wave on the string?
• v FT
  20 N
• ( m / L)
  (.020 kg / m)
• v 32 m/s

19
Question 8

• b) If the string with the linear density of .020
  kg / m under 20.0 N is .75 meters long what is
  the lowest frequency that this string can play?
• v f l
• Fundemental L ½ l
• v f 2 L

20
Question 8

• b) If the string with the linear density of .020
  kg / m under 20.0 N is .75 meters long what is
  the lowest frequency that this string can play?
• v f 32 m/s 21 Hz
• 2L 2 (.75m)

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Question 9
f 256 Hz l 2 L 1.60m V 409.6 m/s
f 512 Hz 2x256 Hz l L .80 m V 409.6 m/s
f 768 Hz 3x256 Hz l 2 / 3 L .53 m V
409.6 m/s
f 1024 Hz4X256 l 1/ 2 L .40 m V 409.6
m/s
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Question 10

• a) Describe or diagram a transverse wave.
• Displacement is perpendicular to wave propagation
• b) Describe or diagram a longitudinal wave.
• Displacement is parallel to wave propagation

23
Question 10

• c) What type of wave is a water wave?
• transverse
• d) What type of wave is a sound wave?
• longitudinal
• e) What type of wave is a wave on a string?
• transverse

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Question 10

• f) v 331 m/s .6 T
• v 331 m/s .6 (20oC) 343 m/s
• Speed of sound is temperature dependent

25
Question 11 first

• 11. The following open end tube has a
• length of .50 m.
• a) What is the wavelength of this wave
• form?
• Since the tube is .50 m and the wave form
  represents a whole wave then the wavelength is
  .50 m

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Question 11 first

• b) What is the frequency of sound produced by
  this tube if the speed of sound is 345 m/s?
• V f l v f 345 m/s 690 Hz
• l .50 m
• Which harmonic does this waveform represent?
• It represents the 2nd harmonic of a open end tube

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Question 11 first

• The following represents the 4th harmonic of a
  open end tube

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Question 11 Second

• 11. The following closed end tube has a
  length of
• .333 m.
• a) What is the wavelength of this wave
  form?
• This wave represents ¾ of a wave. Therefore
• L ¾ l
• or 4/3 L l
• 4/3 (.333 m ) .444 m

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Question 11 Second

• b) What is the frequency of sound produced by
  this tube if the speed of sound is 345 m/s?
• v f l
• v f 345 m/s 777 Hz
• l .444 m

30
Question 11 Second

• Which harmonic does this waveform represent?
• This represents the 3rd harmonic of a closed end
  tube
• d) Draw the 1st harmonic or fundamental
  displacement wave form in the tube below

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Question 11 Third

• Beat frequency problem
• 400 Hz and unknown
• 20 beats per 10 seconds
• Unknown can be 398 Hz or 402 Hz
• 401 Hz and unknow
• 10 beats per 10 seconds 0
• Unknown must be 402 Hz

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Question 12

• a)Why does a 1000 Hz sound with a sound intensity
  of 60 dB sound louder than a 100 Hz also with a
  sound intensity of 60 dB?
• We are more sensitive to 1000 Hz sounds than 100
  Hz sounds. That is why we need bass boosts in
  stereo systems.

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Question 12

• 120 db 80 db 40 / 10 4
• dB is a logarithmic scale in which each 10
  decibel difference is 10 times more intense sound
  wave
• 104 10,000 times more energy reaching the ear
  per meter per second

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Question 13

• a) Why does the frequency of a sound wave appear
  to increase when the source and observer move
  towards each other.
• The Doppler effect explains this phenomenon. The
  relative velocity of the sound increases as the
  observer and the source approach each other. The
  number of peaks per second reaching the observer
  increases and therefore the apparent frequency
  increases.

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Question 14

• f f ( v / - vo)
• ( v - / vs )
• Vo 30 m/s (observer) vs -20 m/s
• This accounts for there relative velocities
  toward each other
• f 500 Hz ( 340 m/s 30 m/s ) 578 Hz
• ( 340 m/s 20 m/s )

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Question 15

• a) What is a sonic boom?
• It is an pressure wave that sounds like
• thunder
• b) How are they produced? they are produced by
  objects traveling above the speed of sound
• c) When are they produced?
• They are produced and released as pressure
  builds up on the surface of an object traveling
  above the speed of sound. This cycle of pressure
  build up and release repeatedly produce sonic
  booms

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Tacoma Narrows Bridge Breaking Glass Comparison

• The Tacoma narrows bridge disaster was caused by
  standing waves produced in its structure by the
  wind which caused the bridge to vibrate at its
  natural frequency. Since the wind was applying a
  force at the natural frequency of the bridge,
  constructive interference occurred until the
  elastic limit of the materials the bridge was
  composed of was reached.

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Tacoma Narrows Bridge Breaking Glass Comparison

• Glass can be made to break if the glass is
  exposed to its natural frequency from a speaker
  or person at a very high amplitude.
• The sound from the person or speaker will cause
  the beaker to undergo constructive interference (
  the glass will resonate ) until the elastic limit
  of the glass is met and it breaks.