# Waves

AQA AS Physics Chapter 12: Waves

Borrowed from someone else's notes.

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## 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

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## Measuring Waves

·        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.

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## Refraction

·

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

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## Difraction

·        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

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## Superposition

·        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.

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## 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

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## 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

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## 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

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