Waves

Longitudinal waves - displacement of particles are parallel to the direction of travel

Transverse waves - the displacement of particles are perpendicular to the direction of travel

·        Plane polarisation occurs when all the vibrations in a wave are made to travel in a single plane

·        Displacement - the distance and direction a particle moves from its equilibrium position.

·        Amplitude - the maximum displacement  of a particle.

·        Wavelength - the distance between two adjacent vibrating particles.

·        Period - the time taken for one complete wave to pass a fixed point.

·        Frequency  - the number of waves passing a given point every second. 

·        The relationship between frequency and period is - time = 1/frequency.

·        The formula for the speed of a wave is -speed = frequency multiplied by wavelength.

The phase difference of a particle is the fraction of the cycle a particle has passed through relative to a given starting point.

·       

     The change in direction due to the change in speed

·        Caused when a wave passes through a different medium

·        For example a light wave from air into glass. Here the wavelength, speed and direction change but the frequency stays the same

·        Diffraction is the bending of a wave around an obstacle or through an opening

·        Smaller the gap the greater the diffraction

·        Longer the wavelength the greater the diffraction

·        The principle of superposition states that when two waves meet the sum of the individual displacements will give the total displacement

·        crest meets crest or a trough meets trough, a supercrest or a supertrough is formed as the two waves reinforce each other creating a constructive interference

·        crest meets a trough a destructive interference is formed

·         If the displacement values are equal then the resultant value is zero as the waves cancel each other out

·         If one displacement is bigger than the other the total displacement becomes smaller.

     Examples of superposition are stationary waves and water waver in a ripple tank. 

·        Produced when two travelling progressive waves of the same frequency and amplitude pass through one another in opposing directions

·        At fixed points along the wave they form points of zero displacement called nodes

·         At maximum displacement the points are called antinodes

·         Adjacent nodes are always 180⁰ out of step

·        When the waves are in phase they reinforce each other and produce a larger wave

      However if they are out of phase then cancellation occurs

·        The phase difference between two vibrating particles is zero if they are between adjacent nodes

·         If the two particles are separated by an odd number of nodes then the phase difference is 180⁰

 NB* that Stationary waves vibrate freely and do not transfer energy

•        Stationary waves have resonant frequencies that occur when there is an antinode at an open end and a node at the other end of a pipe.

•        t = 2L  divided by c = m / f which gives  2L/m = c/f  which is therefore the same as λ

 •        That means stationary waves are formed at frequencies f₀, 2f₀, 3f₀ etc.

 •        The length of the vibrating section of the string L = mλ/2 where m is an integer of half wavelengths.

•   Longer the string the lower the nose because half wavelength at natural frequency is longer

•        Heavier the string the lower the note because waves travel more slowly down the string

  •        The looser the string the lower the note because waves travel more slowly down the string