Standing Waves Flashcards
what is another name for standing waves
stationary waves
what is a stationary wave
- a wave created by the superposition of two progressive waves
- moving in opposite directions
what do the waves need to have in common in order for their superposition to occur
they need to have the same frequency and amplitude
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 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
why
- 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
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
- the points of minimia would be the nodes
- the points of maxima would be the antinodes
what therefore is the definition of a node
a point of zero amplitude within a standing wave
what is the difference between standing and progressive waves in terms of how they handle energy
- standing waves store energy
- whereas progressive waves transfer energy from one point to another
what is the difference between standing an travelling waves in terms of their amplitude
- 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
how do the oscillations themselves differ between stationary and progressive waves
- 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
how can standing waves be created in strings using melde’s experiment
- 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
what would a node in a string look like
the node would be a point on the string which doesnt seem to be vibrating like the rest of the string
why does this method work in the first place with string
- 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
what is a safety precaution that should be taken when doing melde’s experiment
- frequencies in the range 5 to 30 Hz should be avoided
- as they can trigger epileptic fits in some
how could the speed of the incident and reflected waves in the string be calculated
- as you can measure the wavelength yourself
- and you are changing the frequency yourself
- you can use v = f lambda
how do musical instruments like a guitars make sound
- 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
why do string-composed instruments usually have holes in them (resonating sound box) or are plugged in electronically
- as the string only interacts with a small region of air
- they need a resonating sound box or electrical equipment to amplify the sound
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
- v = the root of (T / u)
- T = tension
- u (greek letter mu) = mass per unit length
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
f = 1/2l * root of (T /u)
how do you get that equation for frequency
- 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)
using the variables in that equation, what things would make the frequency greater for stringed instruments in general
- shorter strings
- string with larger tensions
- stringer with lower mass per unit lengths
what is the frequency emitted from a 1st harmonic wave called
the fundamental frequency
what are notes emitted by vibrations other than the fundamental called
overtones
what therefore are harmonics
overtones that have whole number multiples of the fundamental frequency
what is the fundamental factor which allows wind instruments to work
when air is blown into them, standing air waves are formed from vibrations produced in the mouthpiece
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
- 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
what is always produced at the open end of the tube and why (not sound)
- antinodes
- because reflections always produce antinodes
why are nodes always formed at the closed ends of the tubes
because the particles are unable to oscillate
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
- 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
what would be the case if some holes were open rather than all being open or closed
- 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
what is the node and antinode pattern like in the open tubes (wouldve been useful before the previous explanation)
- the beginning and end of the tubes would have antinodes
- with a pattern of alternating nodes and antinodes in between
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
- 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
why does leaking air into the thumbhole result in higher harmonics
- 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
