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Yr 12 Physics 16 - Superposition Of Waves > Standing Waves > Flashcards

Standing Waves Flashcards

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1
Q

what is another name for standing waves

A

stationary waves

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2
Q

what is a stationary wave

A
  • a wave created by the superposition of two progressive waves
  • moving in opposite directions
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3
Q

what do the waves need to have in common in order for their superposition to occur

A

they need to have the same frequency and amplitude

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4
Q

if you have two speakers connected to the same signal generator facing each other, where the midpoint P and the waves interfere constructively here, where, in regards to P, would you expect to have destructive interference

A
  • a quarter of the wavelength to the left and right of P

- with this pattern being followed from these two points every half wavelength they move in their respective directions

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5
Q

why

A
  • if the points are a quarter wavelength away from P (pi / 2)
  • it means the waves from the further speaker would have to travel an extra pi / 2 wavelength
  • whereas the closer one would have to travel pi / 2 of a wavelength less
  • this means that when the waves meet they would be pi wavelengths out of phase (antiphase)
  • resulting in their superpositioning being destructive
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6
Q

what would you call the points of maxima where the sound would be the loudest and the points of minima where it would be the quietest

A
  • the points of minimia would be the nodes

- the points of maxima would be the antinodes

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7
Q

what therefore is the definition of a node

A

a point of zero amplitude within a standing wave

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8
Q

what is the difference between standing and progressive waves in terms of how they handle energy

A
  • standing waves store energy

- whereas progressive waves transfer energy from one point to another

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9
Q

what is the difference between standing an travelling waves in terms of their amplitude

A
  • the amplitude of standing waves varies from 0 at the nodes to a maximum at the antinodes
  • whereas the amplitude of all oscillations along a travelling wave is constant
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10
Q

how do the oscillations themselves differ between stationary and progressive waves

A
  • the oscillations are all in phase between the nodes for a standing wave
  • whereas in a progressive wave the phase varies continuously along the travelling wave
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11
Q

how can standing waves be created in strings using melde’s experiment

A
  • a length of string is attached to an oscillator and passed over a pulley
  • the string is kept taut by weight hanging from its end
  • the frequency of the oscillator is adjusted until nodes and anitnodes are clearly visible
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12
Q

what would a node in a string look like

A

the node would be a point on the string which doesnt seem to be vibrating like the rest of the string

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13
Q

why does this method work in the first place with string

A
  • when a pulse is sent along the rope that is fixed at one end
  • the reflected pulse is out of phase with the incident pulse
  • if a phase change of pi radians takes place at the point of reflection, destructive interference would occur
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14
Q

what is a safety precaution that should be taken when doing melde’s experiment

A
  • frequencies in the range 5 to 30 Hz should be avoided

- as they can trigger epileptic fits in some

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15
Q

how could the speed of the incident and reflected waves in the string be calculated

A
  • as you can measure the wavelength yourself
  • and you are changing the frequency yourself
  • you can use v = f lambda
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16
Q

how do musical instruments like a guitars make sound

A
  • when the string is plucked it produces a standing wave in the 1st harmonic
  • as the string is fixed at two points (nodes) and only consists of half a wavelength
  • the energy in the standing wave is transferred to the air around it which makes the sound
17
Q

why do string-composed instruments usually have holes in them (resonating sound box) or are plugged in electronically

A
  • as the string only interacts with a small region of air

- they need a resonating sound box or electrical equipment to amplify the sound

18
Q

using the setup of a sonometer (basically mimicking the setup of a string on an instrument that has two nodes and 1 harmonic) what would the equation be to work out the speed of the incident and reflecting waves using the mass per unit length of the string

A
  • v = the root of (T / u)
  • T = tension
  • u (greek letter mu) = mass per unit length
19
Q

if you measured the length of the string and wanted to work out the frequency using an alternation of the previous equation, what equation would you use

A

f = 1/2l * root of (T /u)

20
Q

how do you get that equation for frequency

A
  • v= f lambda(Y)
  • so v = root (T/u) = fY = root(T/u)
  • dividing by wavelength gives f = (root(T/u) / Y
  • which = 1/Y * root(T/u)
  • as the 1st harmonic is half a wavelength and you have l, the length of the string, it means that Y/2 = l, aka Y = 2l
  • replacing the 1/Y with 1/2l
  • making f = 1/2l * root(T/u)
21
Q

using the variables in that equation, what things would make the frequency greater for stringed instruments in general

A
  • shorter strings
  • string with larger tensions
  • stringer with lower mass per unit lengths
22
Q

what is the frequency emitted from a 1st harmonic wave called

A

the fundamental frequency

23
Q

what are notes emitted by vibrations other than the fundamental called

A

overtones

24
Q

what therefore are harmonics

A

overtones that have whole number multiples of the fundamental frequency

25
Q

what is the fundamental factor which allows wind instruments to work

A

when air is blown into them, standing air waves are formed from vibrations produced in the mouthpiece

26
Q

a small speaker connected to a signal generator can be used to set up standing waves in tubes open at one or both ends. how would this be done and how would you know when a standing wave has been produced

A
  • the frequency would be slowly increased by adjusting the signal generator
  • when a standing wave is formed the air in the column resonates
  • this produces an intense booming sound
27
Q

what is always produced at the open end of the tube and why (not sound)

A
  • antinodes

- because reflections always produce antinodes

28
Q

why are nodes always formed at the closed ends of the tubes

A

because the particles are unable to oscillate

29
Q

why do notes have to be played on wind instruments by opening or closing holes along the length of it and blowing into a mouthpiece, like a recorder

A
  • the air is free to move when the holes are open
  • so at resonance there will be antinodes at the hole
  • with all holes closed there would be antinodes at the mouthpiece and end of the recorder
  • causing the wavelength of the lowest fundamental to equal twice the length of the instrument
30
Q

what would be the case if some holes were open rather than all being open or closed

A
  • with some holes open the the fundamental frequency will be that of the standing wave
  • with antinodes at the mouthpiece and the closest open hole
31
Q

what is the node and antinode pattern like in the open tubes (wouldve been useful before the previous explanation)

A
  • the beginning and end of the tubes would have antinodes

- with a pattern of alternating nodes and antinodes in between

32
Q

why is the wavelength of the lowest fundamental equal to twice the length of the instrument in the recorders case if no holes are open

A
  • because due to both ends of the recorder being open
  • there wold be antinodes at each end and only one node in the middle of it
  • meaning that if a wave were to obey this it would create half a wavelength across the length of the recorder (going from the top to reaching the middle of the recorder then reaching the other antinode at the bottom of it)
  • aka, the whole wavelength of this lowest fundamental would be twice the length
33
Q

why does leaking air into the thumbhole result in higher harmonics

A
  • because it divides the air column into two
  • which means the wavelength is halved so the frequency is doubled (v = fY)
  • this causes the pitch of the emitted note to increase

Yr 12 Physics 16 - Superposition Of Waves (4 decks)

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