Waves Flashcards
Amplitude
Amplitude (A) is the maximum distance a particle is displaced from its rest position.
- The greater the amplitude of a wave, the more energy it is carrying.
Wavelength
Wavelength (λ) is the distance between two successive corresponding positions in a wave
Frequency
Frequency (f) is the number of waves passing any point each second, measured in hertz (Hz)
Period
Period (t) is the time taken for one wave to pass any point, measured in seconds (s)
Energy transfer of waves
Energy can be transferred by the wave motion between two places. The direction of proapgation of the wave is in the same direction as the energy flow.
- Waves can not transfer matter (eg. particles and mass).
Sound waves
Sound waves require vibrating air particles to propagate.
Eg. A speaker
- When a speaker produces music, it vibrates back and forth. As it moves forward, it pushes on the closest air particle, whch, in turn, pushes on the next air particle (and so on).
- As the speaker moves backward, it pulls the closest air particle with it, which, in turn, pulls on the next air particle (and so on).
- Vibrating air particles cause any neighbouring air particles to vibrate and so on
- Once the air particles closest to your ear begin to vibrate, they will then vibrate your eardrum. This will be interpreted by your brain as sound. Thus, the sound energy has been transferred from the speaker to your ear by vibrating air particles.
Mechanical wave
A mechnical wave is a wave that requires a medium to travel, and therefore cannot travel through a vacuum.
- Mechanical waves are either transverse or longitudinal (eg. sound waves, water waves, waves made on ropes/string/springs and earthquakes).
Pulse
The single movement of a particle
- The pulse of a sound will be transferred through the air by each individual partice of air undergoing on vibration (backwards and forwards movement).
Transverse waves
In transverse waves, particles move perpendicular to the motion of the wave.
- The motion of the individual particles in the medium is a temporary displacement of mass, as the particles (and their mass) will return to their starting position after the wave motion has stopped. The crest and trough of a wave are the points of maximum displacement of the particles in the medium.
Longitudinal waves
In longitudinal waves, particles move parallel to the motion of the wave.
- The areas of compression in the wave are where many particle come together and create regions of higher pressure. The areas of rarefaction in the wave are where many particles spread apart and create regions of lower pressure.
Electromagnetic wave
An electromagnetic wave is a wave that does not require a medium to travel, and can therefore travel through a vacuum.
- Electromagnetic waves are produced when electrons are made to accelerate, or when electrons change energy levels in an atom.
- Radio waves, microwaves, infrared, ultraviolet, x-rays and gamma rays
- Maximum speed is 3 x 10^8 ms^-1
How is energy transferred in a transverse wave?
In transverse waves, particles move perpendicular to the motion of the wave. Assuming the wave is moving from left to right, the particle closest to the wave source will be moved up and down, and pull any neighbouring particles with it. As the first particle pulls on its neighbouring particles, it will transfer some of its energy to the particle being pulled. This will cause the first particle to slow down and eventually stop, as the neighbouring particle is being pulled.
In turn, the neighbouring particle will pull on its neighbours and transfer its energy. Because of this, all of the particles will be moving up and down as the wave passes by, and the energy will be transferred between the particles to follow the wave motion.
How is energy transferred in a longitudinal wave?
In longitudinal waves, particles move parallel to the motion of the wave. Assuming the wave is moving from left to right, the particle closest to the wave source will be pushed from left to right, as region of higher pressure has been created by the source. As the first particle is pushed, it then creates a region of higher pressure next to its neighbouring particles, which pushes those air particles. As the first particle pushes its neighbouring particles, it will transfer some of its energy to the particle being pushed.
In turn, the neighbouring particle will create regions of higher pressure, push on its neghbours and transfer its energy. Because of this, all of the particles will be moving from left to right as the wave passes by, and the energy will be transferred between the particles to follow the wave motion.
Wavefronts
A wavefront represents the leading edge of one complete wave.
- A ray is the direction of travel of a wave front (drawn as an arrow)
- Wavefronts are at right angles to rays
- Wavefronts must remain parallel, therefore, a wave changes direction as it changes speed entering or leaving a medium.
‘In phase’
Points along a wave are ‘in phase’ if they undergo similar motion at the same time.
- Points ‘in phase’ are a whole number of wavelengths apart.
- Phase is measured as an angle. ‘In phase’ means a phase difference of 0°.
‘Out of phase’
Points along a wave are ‘out of phase’ if they move oppositely to each other.
- Points ‘out of phase’ are an odd number of half wavelengths apart.
- Phase is measured as an angle. Exactly ‘out of phase’ means a phase difference of 180°.
Calculating phase difference
- Determine how far of a wavelength apart the points are as a fraction
(eg. 1/4 of a wavelength) - Multiply the fraction by 360°
(eg. 1/4 x 360° = 90°)
(Therefore, points A and B. have a phase difference of 90°).
Reflection and transmission of a pulse
Heavy string to light string
Heavy string to light string
- Pulse moves slower along heavy string and faster along the light string.
- A small pulse reflected and the same way up as the original pulse moves back along the heavy string.
- The amplitude will be smaller when reflected due to a decrease in energy (as not all the energy is reflected).
Reflection and transmission of a pulse
Light string to heavy string
Light string to heavy string
- Pulse moves slower along heavy string and faster along the light string.
- A small pulse reflected and upside down to the original pulse moves back along the light string.
- The amplitude will be smaller when reflected due to a decrease in energy (as not all the energy is reflected).
- As the pulses in the light string are travelling faster, they are further from the boundary when reflected.
Light waves
The wave model of light describes light as consisting of waves with a very small wavelength and travelling in straight lines from a source with a very large speed.
- When light passes from one medium to another (eg. from air to glass), some light is reflected and some is refracted into the second medium.
- When light passes from one medium to an optically denser one (eg. from air to glass), the speed of the light decreases.
Refraction of plane waves at a straight boundary between deep and shallow water
- The waves angle of incidence (measured with respect to the normal) θ1 equals the angle that the incident wavefronts make with the boundary.
- The waves angle of refraction θ2 equals the angle that the refracted wavefronts make with the boundary.
- Water waves will change direction at a boundary between deep and shallow water. The waves will slow down as they enter the shallow water which will cause the wavelengths to shorten.
Equation for wave refraction
1n2 = sin θ1 / sin θ2 = v1 / v2 = λ1 / λ2
Where,
- 1n2 is the relative refractive index (constant)
- v1 / v2 is the ratio of the wave speeds
- λ1 / λ2 is the ratio of the wavelengths
(Note - the frequency of a wave does not change when it is refracted)
Wave equation
- For wave velocity
(with time)
v = λ/t
Where,
- v is the wave velocity
- λ is the wavelength
- t is the period
Diffraction of waves
- Diffraction is the process of waves spreading as they pass through a gap
- Maximum diffraction occurs when the wavelength (λ) is approximately equal to the size of the gap.
- The wavelength of a wave does not change when it is diffracted.
eg. Sound waves have a longer wavelength compared to light waves. Because of this longer wavelength, the soundwaves can diffract around barriers through openings (as they are the same order of size as the wavelength of the sound waves). Comparatively, lightwaves cannot diffract as much as sound around barriers. Therefore, often people can hear objects, but not see them.
When waves pass through a gap, the waves are striking the ends of two barriers. The waves which pass through the gap bend behind both barriers.
Sound waves
When sound waves reach the ear, they cause the eardrum to vibrate rapidly. The sensation of loudness experienced depends on the intensity of the sound waves that reach the listener’s ear.
- The itensity of sound is related to the rate of flow of energy. A louder sound wave has a greater amplitude.
- The pitch of the sound is related to the frequency of the wave.
Speed of sound
In air at 0°C, the speed of sound is 331 ms^-1
In water at 20°C, the speed of sound is 1,480ms^-1
- Sound travels slower than light.
Superposition
Superposition is the ability of waves to superimpose (add their displacements and their energy) as they move through each other.
(Eg. two rectangular pulses moving in opposite directions can pass through each other so that each pulse remains the same afterwards. The principle of superposition allows the two waves to be ‘added’ together by adding their displacements together at each instant in time.)
Constructive superposition
Constructive superposition is the case where two pulses are the same way up and their displacements add.
Deconstructive superposition
Deconstructive superposition is the case where two pulses are inverted with respect to each other and their displacements subtract to give 0.
Constructive interference
Areas of constructive inference are darkened areas where trough meets tough, and lightened areas where crest meets crest.
Deconstructive interference
Areas of deconstructive inference are areas between lightened and darkened areas of constructive inference where crest meets trough.
- Areas of deconstructive inference are where undisturbed water exists.
Interference
Wave interference occurs when two waves meet while travelling along the same medium.