Everything that I know about waves
Wave definition – a transfer of energy that results in no net transfer of matter
Mechanical waves – recquire a medium to travel through eg sound, water waves
Electromagnetic waves – don’t recqurie a medium to travel through, can travel
through a vacuum eg light and radio waves
Longditudinal waves – the movement of parti is parallel to the direction of wave
propagation eg sound
Transverse wave – the motion of particles is perpendicular to the direction of wave
propagation eg light, water waves
Graphs of waves can be done on a displacement time graph, displacement distance
graph for transverse waves
For longditudian waves it is a pressure distance graph norusually or pressure time,
as this creates the same graph as the transverse one. Compressions are when the
particles are close together and rarefractions when far apat.
The wavelength is the distance that one full cycle of a wave takes up. It is the
distance between 2 parties of a wave that are in phase eg two troughs and two
crests
Period – the time that is takes for 1 full cycle of a wave
Frequency – the number of full cycles of a wave that occur in 1 second
Amplitude – the maximum displacement of particles from the equilibrium position.
The period and the frequency are inversely related f = 1/t
The speed of a wave is equal to the wavelength multipled by the frequency of the
wave
If waves encounter a fixed boundary then they are inverted and reflected, they retain
all of their existing properties. If they encounter a loose boundary then the wave is
reflected and travels in the opposite direction but it isn’t inverted.
When a wave encounters a change in medium it can be absorbed, reflected or
transmitted.
When waves are reflected then they bounce of a smooth surface. The angle of
incidence is equal to the angle of reflection. The normal is perpendicular from the
surface at the point of impact. The incidence ray is the first ray and the reflected ray
is the one after reflection. The angle of incidence is between the incident ray and the
normal and the angle of reflection is between the normal and the reflected ray. When
reflection has occurred all of the properties of the wave are maintained, except
amplitude which can decrease. If the surface is smooth than the reflection will be
clear, if inconsistent the reflection will be scattered.
A wave front shows lines that represents all of the waves that are in the same phase
eg all have crests or all have troughts.
Refraction occurs when a wave changes medium. If the wave enters a more dense
medium then it will usually travel slower. If the wave travels slower than it will bend
towards the normal. If the wave travels faster due to entering a less dense medium
then it will bend away from the normal. After refraction occurs the speed of the wave
changes however the frequency remains constant meaning that it is the wavelength
that must change. Hotter air is less dense and therefore sound travel faster in it.
Once again the normal is perpendicular to the surface and the bending is against
where the wave would have gone if it had not changed mediums
Diffraction occurs when a wave encounters an aperture of an obstacle and bends
around it. This occurs due to Huygens principle which states that every particles in a
wave emits a secondary wave which all cancel out to create the resultant wave.
Therefore when the wave encounters the gap the waves no longer cancel out
causing the circular motion to occur. If the aperture is smaller then the diffraction will
be more significant. If the length of the obstacle is smaller than the diffraction will ve
more significant.
When two waves cross over each other than their displacements are momentarily
added together for the resultant wave which is created. This can cause constructive
interference where the ampltiudes are added together to create a higher amplitude
or destructive where one amplitude is subtracted from the other causing a drop in
ampltidue. Complete destructive interference results in 0 ampltide. Constructive
interference is also called superposition.
Standing waves occur when the resultant wave created by interference appears to
have no lateral movement. A standing wave occurs when the wave with the exact
same properties is allowed to interfere and travelling in opposite directions, however
they will only form in a string or an open pipe if the length of the stirng is a multiple of
half wavelengths and in a closed pipe is a multiple of quarter wavelengths.
The standing wave has both displacement nodes – where 0 dispakcemnt occurs due
to complete destructive interference occurin and antinodes where complete
constructive interference occurs.
The lowest frequency required to create a standing wave is called the fundemendal
frequency.
In increasing frequency they are called harmonics with 2nd harmonic being second
lowest third harmonic third lowest etc. erd harmonic is 3 times the fundemantal
frequeny. They can also be called overtones, for the number that they are above the
fundamental eg the 3rd harmonic is called the second overtone.
In a string there is displacement nodes at ever end as they are fixed ends and fixed
ends are always nodes. At open ends there are always displacement anti nodes. For
the string and open pipe the length of the wavelength is equal to 2 x the length of the
pipe divided by the harmonic number. For the closed pipe the length of the tube is
equal to nx wavelength/4. Only odd number harmonics exist for the closed pipe. This
is because there must be a antinode at the open end and a node at the closed which
limits the number of harmonics that can be formed.
The frequency of the beat is found from the absolute value of the frequency of the
first – the frequency of the second sound that makes up the beat.
Resonance occurs when an object vibrates at its natural frequency causing the
increase in amplitude of the waves involved. This is due to the formation of standing
waves whose constructive interference causes the increase in amplitude.