Standing Waves

Question 1

what is another name for standing waves

Answer 1

stationary waves

Question 2

what is a stationary wave

Answer 2

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

Question 3

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

Answer 3

they need to have the same frequency and amplitude

Question 4

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

Answer 4

• 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

Question 5

why

Answer 5

• 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

Question 6

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

Answer 6

• the points of minimia would be the nodes

- the points of maxima would be the antinodes

Question 7

what therefore is the definition of a node

Answer 7

a point of zero amplitude within a standing wave

Question 8

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

Answer 8

• standing waves store energy

- whereas progressive waves transfer energy from one point to another

Question 9

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

Answer 9

• 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

Question 10

how do the oscillations themselves differ between stationary and progressive waves

Answer 10

• 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

Question 11

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

Answer 11

• 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

Question 12

what would a node in a string look like

Answer 12

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

Question 13

why does this method work in the first place with string

Answer 13

• 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

Question 14

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

Answer 14

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

- as they can trigger epileptic fits in some

Question 15

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

Answer 15

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

Question 16

how do musical instruments like a guitars make sound

Answer 16

• 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

Question 17

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

Answer 17

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

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

Question 18

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

Answer 18

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

Question 19

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

Answer 19

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

Question 20

how do you get that equation for frequency

Answer 20

• 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)

Question 21

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

Answer 21

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

Question 22

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

Answer 22

the fundamental frequency

Question 23

what are notes emitted by vibrations other than the fundamental called

Answer 23

overtones

Question 24

what therefore are harmonics

Answer 24

overtones that have whole number multiples of the fundamental frequency

Question 25

what is the fundamental factor which allows wind instruments to work

Answer 25

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

Question 26

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

Answer 26

- 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

Question 27

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

Answer 27

- antinodes | - because reflections always produce antinodes

Question 28

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

Answer 28

because the particles are unable to oscillate

Question 29

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

Answer 29

- 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

Question 30

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

Answer 30

- 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

Question 31

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

Answer 31

- the beginning and end of the tubes would have antinodes | - with a pattern of alternating nodes and antinodes in between

Question 32

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

Answer 32

- 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

Question 33

why does leaking air into the thumbhole result in higher harmonics

Answer 33

- 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