Waves and Vibrations
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.
Stationary and Progressive Waves
· 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
Stationary and Progressive Waves ctd
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 and Progressive Waves ctd (2)
• 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