waves Flashcards
progressive waves (aka travelling waves)
these are waves which transfer energy from one place to another, but not matter - particles of matter oscillate about equilibrium but do not travel with the wave (e.g. sound, light and earthquakes
longitudinal waves (aka compression waves)
waves in which oscillations are parallel to the direction of energy transfer (e.g. sound waves and earthquake P-waves) - they have alternate compressions and rarefactions of the medium through which the wave is travelling
transverse waves
waves in which oscillations are perpendicular to the direction of energy transfer (e.g. light, ripples in water, all electromagnetic waves, and S-waves)
amplitude (A(m))
the maximum displacement from the equilibrium position; it can be positive or negative
displacement (S(m))
the distance from the equilibrium position in a particular direction; a vector, so it can have either a positive or negative value
wavelength (λ(m))
the minimum distance between two points in phase on adjacent waves (e.g. the distance from one peak to the next, or from one compression to the next)
time period of oscillation (T(s))
the time taken for one compete oscillation; the time taken for a wave to move one whole wavelength past a given point
frequency (f(Hz/s^-1))
the number of wavelengths passing a given point per unit time
phase
A measurement of the position of a certain point along the wave cycle
phase difference
the amount by which one wave lags behind another wave
wave speed (V or c (ms^-1))
the distance travelled by the wave per unit time; wavelength x wave frequency
relationship between frequency and time period
they are inverse; 1 = T x f
phase difference (measured in degrees or radians)
The amount one wave lags behind another as a proportion of the wavelength.
oscilloscope (cathode ray)
Measures voltage, displaying waves from a signal generator as a function of voltage over time - these waves are called traces. Sources of waves could be produced by plugging in an AC supply; or a microphone which converts sound waves into electrical signals.
markings on an oscilloscope
Vertical divisions = voltage/amplitude of the wave (controlled by gain dial)
Horizontal divisions = time (can be used to find time period and frequency; controlled by timebase dial).
wave refraction
when a wave bends at a boundary between two materials due to the difference in density causing it to speed up or slow down
polarised waves
waves oscillating along only one axis
unpolarised waves
waves oscillating in any direction perpendicular to the axis of propagation
plane of polarisation
the plane in which the wave vibrates
wave diffraction around obstacles
where waves meet obstacles, they will diffract around the edges, but there would be a shadow behind the obstacle where the wave is blocked - the wider the obstacle compared to the wavelength, the less diffraction that would occur, so the longer the shadow
plane polarisation
when a plane is polarised so that it only oscillates in one direction, e.g. using a polarising filter - this is only possible for transverse waves
reflection
when waves are bounced back after hitting a boundary and the angle of incidence is equal to the angle of reflection
intensity (eqn i.t.o power)
power / area
intensity
the rate of flow of energy per unit area at right angles to the direction of travel, measured in Wm^-2
relationship between intensity and amplitude
Intensity is proportional to amplitude2 - this is because intensity is proportional to energy, and the energy of a wave depends on amplitude^2
range of wavelengths for visible light
300-700nm
speed of EM waves in a vacuum
3 x 10^8 m/s (‘the speed of light’)
refraction
when a wave changes direction as it enters a different medium - it will bend towards the normal when slowing down (entering a more optically dense medium) and will bend away from the normal when speeding up (entering a less optically dense medium) - this is because the wavelength of the wave is changing and the frequency stays constant
wave speed
frequency x wavelength
refractive index
the ratio between the speed of the wave in a vacuum, c, and the speed of the wave in the medium, v. Therefore, n = c/v.
refractometer
a device used to accurately measure a material’s refractive index by shining a beam of light through a sample, which could then be viewed through a microscope to measure the angle of refraction
refractive index (eqn)
c (speed of light) / v (velocity in the material)
critical angle
the angle of incidence at which the light will reflect off a boundary rather than refracting in the medium
critical angle (eqn)
sinC = 1/n (refractive index)
constructive interference
The interference that occurs when two waves combine to make a wave with a larger amplitude - this will happen when the two waves are in phase, so they are at the same point in a wave cycle (phase difference = 0 or multiple of 360)
principle of superposition
When two or more waves meet, the resultant displacement equals the vector sum of the individual displacements.
superposition
When two waves meet, the resulting displacement is the sum of the individual displacements.
Young’s double slit experiment
A single source of light directed towards a double slit, which creates two coherent beams of light. This interferes as it hits the screen and creates an interference pattern.
destructive interference
The interference that occurs when two waves combine to make a wave with a smaller amplitude; and the two waves must be perfectly out of phase (at odd multiples of 180)
path difference for constructive interference
nλ
coherence
the difference in distance that two waves have travelled in terms of the wavelength (units of length)
path difference for destructive interference
(n+0.5)λ
why are lasers used in experiments?
they produce monochromatic (same wavelength/colour) light
stationary waves on a string
By attaching a vibration transducer on one end of a stretched string when the other end is fixed, this can create a wave by vibrating the string according to a given wave frequency from a signal generator. By alternating the signal generator a bit, it can be adjusted so that there is an exact number of waves in time in which it gets to one end and back, so that the original and reflected waves reinforce each other at resonant frequencies - this would cause an exact number of half λs to fit onto the string. Each particle vibrates at right angles to the string.
wavelength of light (eqn i.t.o split spacing and distance to the screen)
( a (split spacing)* x (fringe spacing)) / D (distance to screen)
stationary wave experiment example
Use an oscillator to pass a wave along a string which is fixed at one end.
The stationary wave will form when the progressive wave is reflected off the fixed end.
evidence for the wave nature of light
By showing that light is able to both diffract and interfere, which are both uniquely wave properties.
maximum number of fringes produced
n (number of fringes) * λ (wavelength) = D (distance) sinθ (between central maxima)
stationary waves
waves that consist of alternating fixed pattern of nodes (points with zero amplitude) and antinodes (points with maximum amplitude). No energy is transferred across the wave.
diffraction of white light
produces a mixture of colours, with the 0th order remaining white and each order becoming a spectrum, with red light being diffracted the most compared to violet light because it has a much larger λ and λ is proportional to sin theta
requirements for a stationary wave
- coherent waves
- must be travelling in opposite directions
harmonic
a point where the stationary wave form doesn’t change because the waves in each direction are reinforcing each other
A point with no vibrations in which the resultant amplitude is 0.
A point with maximum vibration in which the resultant amplitude is at maximum.
first harmonic
when a standing wave is operating at the lowest possible resonant frequency, with only half λ
similarities between stationary and progressive waves
both have wavelength, frequency and an amplitude
stationary waves in wind instruments (or other air columns)
At some frequencies, resonance occurs so a stationary wave would be set up, with nodes forming at the closed end of instruments (usually with the lowest frequency at λ/4), and antinodes forming at the open ends of piper (where both ends are open, the lowest resonant frequency would be at λ/2).
key difference between stationary and progressive waves
in stationary waves, energy is not transmitted from one place to another
stationary waves with microwaves
Microwaves could be produced by a microwave transmitter, which would therefore lead to them being reflected off a metal reflecting plate back towards the transmitters, and as the distance between the two is adjusted, the waves can interfere and set up a stationary wave, and the nodes/antinodes could be found by moving the receiver between the two.
