chapter 8

Question 1

what is periodic motion?

Answer 1

• the basis from which we can develop a theory of waves. It refers to a form of motion defined relative to a midpoint, from which an object is first displaced by a certain distance then moves back to the midpoint, is displaced by the same amount in the opposite direction and returns to the midpoint, at which point the cycle begins again

Question 2

based on this curve, we can define several important parameters:

Answer 2

• the extent of displacement (|y|) is referred to as the amplitude of the motion
• the period of the motion is defined as the time T which separates adjacent peaks
• the frequency of the motion is defined as 1/T (Hz) and 1 Hz is equal to 1s^-1

Question 3

two objects in periodic motion can have the same frequency but still be out of sync. this is known as?

Answer 3

• being out of phase

Question 4

the phase difference between 2 objects in motion can be visualized as?

Answer 4

• the time difference (deltaT) between x-intercepts on graphs of their motion over time

Question 5

Periodic motion involves a constant interchange between kinetic energy and potential energy so it is tied to?

Answer 5

• conservation of energy
  
  • At the peak of an objects motion, its velocity is zero and all of its energy is in the form of potential energy (mgh for a pendulum and 1/2kx² for a mass on an ideal spring). when it passes through the equilibrium point (y=0), its energy is entirely in the form of kinetic energy (1/2mv²) and then is again converted to PE at the opposite peak

Question 6

in both of the classic exmaples of periodic motion (mass on a spring and a pendulum in motion), periodic motion is maintained by a?

Answer 6

• restoring force that acts to pull the object back towards the equilibrium point
  
  • in the case of mass on a spring, the restoring force is expressed by Hooke’s law: F = -kx
  • in the case of a pendulum, the restoring force is gravity (mg)
    
    • for mass on a spring, T = 2π (square root of m/k). a large T indicates a low frequency and this means that a spring with a mass attached to it will oscillate quickly if it has a small mass and a relatively large value of k, whereas it will oscillate slowly if it has a large mass or a small value of k
    • for a pendulum. T = 2π(square root of L/g). the period of a pendulum is only related to its length, with a longer pendulum having greater periods and lower frequencies

Question 7

What are mechanical waves?

Answer 7

• waves that involve the actual physical motion of particles
  
  • can be subdivided into transverse and longitudinal waves

Question 8

what are transverse vs longitudinal waves?

Answer 8

• transverse waves are like classic wave
• longitudinal waves are mechanical waves in which the particles move in the same direction in which the wave propagates and results in a pushing-pulling motionm which is why these waves are sometimes known as compression waves

Question 9

the sptail interval over which a waveform repeats itself is known as its?

Answer 9

• wavelength (lamda)

Question 10

the speed with which a wave signal spreads through space is known as its?

Answer 10

• propogation speed
  
  • depends on the medium

Question 11

propoagation speed, wavelength and frequency are related in the following equation:

Answer 11

• v = (lamda)/frequency
  
  • lamda is the wavelength (m)
  • f is the frequency (s^-1)
  • v is the propagation speed (m/s)

Question 12

what doesn’t change when a wave enters a new medium?

Answer 12

• the frequency
  
  • so wavelength changes (a higher speed of propagation is associated with a greater wavelength)

Question 13

when multiple waves are present in a given location, they exhibit?

Answer 13

• interference
  
  • the amplitudes associated with each wave at a given location add together to predict the behaviour of a particle, which then itself can be modeled as part of a wave
    
    • when overlapping waves have amplitudes with the same directionality, the amplitude of each component wave add up, maining that the product wave exhibits an amplitude greater than that of any of its component waves (constructive interference)
    • when overlapping waves have amplitudes with the opposite directionality, they tend to cancel each other out to some extent (destructive interference)

Question 14

what happens when waves hit a barrier?

Answer 14

• the waves will reflect back at an angle equal but opposite to the angle with which they hit the barrier

Question 15

what is sound made up of?

Answer 15

• longitudinal, compressive waves

Question 16

how do we sense sound?

Answer 16

• in terms of pressure which has units of F/A (force divided by area)

Question 17

sound waves move more quickly through?

Answer 17

• relatively non-compressible, or stiffer media

Question 18

the degree to which a material resists compression is measured via the?

Answer 18

• bulk modulus (B)
  
  • measures how much pressure is needed to compress a substance by a certain amount
    
    • high values of B indicate non-compressibility
      
      • the equation for the speef of sound also depends on density (rho):
        
        • v_sound = (square root of B/rho)
          
          • sound moves fast through extremely incompressible solids, slower through liquids and much more slowly than hases

Question 19

the intensity (I) of sound waves is defined as?

Answer 19

• a measure of the power delivered by sound over a given area, or as watts deivided by meters squared (W/m²)
  
  • the most important modifiable parameter that affects intensity and loudness is amplitude, as intensity if proportional to the amplitude sqyared
  • although the SI units for intensity are W/m², for most practical purposes, intensity is measured in terms of decibels (dB)
    
    • dB = 10log(I/I₀)
      
      • I is the intensity of a given sound in W/m²
      • I₀ is the reference value of 1x10^-12 W/m²
      • take log of number then multiply by 10

Question 20

what does pitch refer to?

Answer 20

• refers to our perception of a sound as high or low, with high-frequency sounds corresponding to high-pitch and low-frequency sounds coresponding to low pitch

Question 21

What happens if the sound source, observer, or both are in motion?

Answer 21

• this is known as the Doppler effect

Question 22

What happens if a source sound is moving while the observer remains still or if the source sound is still but the person moves closer to it?

what happens if both the observer and source are moving?

Answer 22

• As the observer moves closer to the source, the waves ‘bunch up’, resulting in a higher perceived frequency, and as the observer moves awaym it will take longer for them to perceive each wave, resulting in a lower perceived frequency
• the change in perceived frequency is proportional to the degree to which the velocity of the source and/or observer adds to the propagation speed of the wave (changing v while holding lamda constant which means frequency has to change)
  
  • f = f₀ = (v_sound + v_observer)/(v_sound + v_sourve)
    
    • if the observer and sourve are moving towards each other, the perceived frequency will increases so the top must be greater than the bottom
    • if the observer and the source are moving away from each other, the perceived frequency will decrease so the top must be smaller than the bottom

Question 23

the Doppler effect is specifically applied in a technique known as?

Answer 23

• Doppler ultrasonography
  
  • where frequency shifts are utilized to determine whether blood is flowing towards or away from the transducer

Question 24

stable patterns of interference among waves proagating in opposite directions results in what is known as?

Answer 24

• standing waves
  
  • stable wave-like product of multipe waves
  • a standing wave will generally be sinusoidal in shape and have areas where there is no displacement and areas with maximal displacement, corresponding to the amplitude of the resultant standard waves. the points of zero displacement are refered to as nodes and the points of maximum displacement are knwon as antinodes
    
    • as we increase the number of antinodes present in the standing wave, it’s as if we’re compressing more waves into the same sapce so the frequency of the waves is increasing and the wavelnegth is decreasing

Question 25

the standing waveform in a taut string with only one antinode is the lowest-freuqnecy possible standing node, and is defined as the fundamental frequency of teh string and is also known as?

Answer 25

• the first harmonic
  
  • the standing wave that contains 2 antinodes is known as the second harmonic, the wave that contains 3 antinodes is defined as the third harmonic, etc.

Question 26

we obtain the following formula for the wavelength of the nth harmonic in a taut string:

Answer 26

• lamda = (2/n) L
  
  • since v = lamda • frequency, we can express the wavelength as lamda = v/f and sub it into this equation to get: f = (2/n) v/L

Question 27

In a pipe with 2 open ends, both ends would be antinodes. the wavelengths corresponding to each harmonic follow the same pattern, lamda = (2/n)L that we saw for taut strings. the only difference has to do with?

Answer 27

• the relative distribution of nodes and antinodes and how they correspond to each harmonic.
  
  • in a taut string, the nth harmonic has n antinodes whereas in an open pipe, the nth harmonic and n nodes

Question 28

the geometry of a pipe with one closed end (closed pipe):

Answer 28

• the closed end corresponds to an nose and the open end corresponds to an antinode
  
  • the lowest frequency standing wave that satisfies this parameter will have a wavelength 4 times the length of the tube
  • the second harmonic will incorporate 2 antinodes, corresponding to 3/4 of the wavelength and the third componenet will contain one full wavelnegth and one fourth the next one (i.e. five-fourths of a wavelength, and so on)
    
    • these observations can be extended into the following formulas:
      
      • lamda - 4L/n_odd
        
        • f = (n_odd/4) (v/L)
          
          • only work for odd values of n