NCEA Level 3 System of Waves

Standing waves

Formed by two travelling waves of same frequency and amplitude travelling in opposite directions.

Diffraction

The bending and spreading of waves when they pass around an obstacle or through an opening.

Constructive interference

Causes sound to be louder, where bright fringes form, where waves are in phase, and path difference is integer multiple of λ.

Destructive interference

Causes sound to be quieter, where dark fringes form, waves out of phase, and path difference is odd half-integer multiple of λ (n + 1/2)λ.

Doppler Effect

Perceived change on how sound heard changes due to motion of source of sound.

Frequency

Measure of waves per second (Hz)

Beats

Two sounds with slightly different frequencies play a throbbing sound due to interference of sounds. (Quiet = destructive, loud = constructive)

Path difference

Difference in physical distance travelled by two waves from their respective sources to the point where they meet.

Closed pipe standing wave

Formed when two travelling waves interfere, these two waves being the same but one has been reflected off closed end.

Nodes

Form when initial wave and reflected wave meet 180° out of phase, causing destructive interference (0 amplitude and displacement)

Antinodes

Form when two waves are in phase causing constructive interference (maximum displacement and amplitude)

Closed pipe requirements

Must have node at one end and antinode at other end. Odd-numbered harmonics meet these conditions but even-numbered harmonics do not. Hence why all harmonics cannot be formed.

Odd-numbered Harmonics

Antinode on one end and node on the other

Even-numbered harmonics

Must begin and end with either node or antinode (node and node or antinode and antinode)

nλ

path difference

Width of Double Slits (compared to diffraction grating)

Wider maxima due to less sources of light = less interference = larger area of constructive interference

Brightness of Double Slits (compared to diffraction grating)

Dimmer maxima due to fewer waves constructively interfering,

Pattern change of Double Slits (compared to diffraction grating)

More gradual change due to less sources of light = less interference = larger area of constructive interference.

Smaller λ

Light with smaller λ will diffract at smaller angle

Doppler effect moving towards

Each wave emitted is from a closer position, compressing the λ meaning more waves reach listener per second.

Doppler effect moving away

Each wave emitted is from a further position, stretching the λ meaning fewer waves reach listener per second.

Source of waves is perpendicular to listener

For a moment the true frequency is perceived due to there being no relative velocity towards the listener.

Amplitude

Maximum displacement from equilibrium

Wavelength

Physical distance over which the wave’s pattern repeats.

Crest

Maximum positive point of displacement

Trough

Maximum negative point of displacement from equilibrium