Superposition Superposition is the ability of waves to superimpose (add displacements & energy) as they move through each other. Constructive interference. Approaching Overlapping Receding

Destructive interference . Approaching Overlapping Receding

Combining waves of the same f What happens when two waves are present at the same place at the same time?

The Principle of Interference / Superpositioning For waves: The resulting wave = the sum of the individual waves Constructively Destructive This applies to all waves: water, light, sound, etc.

Interference: What happens when two waves pass through the same region? When two crests overlap it is called constructive interference. The resultant displacement is larger then the individual ones. When a crest and a trough interfere, it is called destructive interference. The resultant displacement is smaller.

Phase Two quantities are in phase if they are simultaneously increasing or decreasing, eg V & I are in phase in an AC circuit Waves in phase

Crest of one wave coincide with the trough of the other wave. 2 waves out of phase by ½ a cycle or 180o. Crest of one wave coincide with the trough of the other wave.

Waves out of phase by 90o or a ¼ cycle If there is a period of time where one quantity is increasing while the other is decreasing they are out of phase. The two quantities need to have the same frequency (f) but not necessarily the same amplitude to stay in phase. Waves out of phase by 90o or a ¼ cycle

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Beats is a regular pulsing of the loudness of a sound which is heard when two sources produce sounds of slightly different frequency. fbeat = f1 – f2 For example, when a 552 Hz and a 556 Hz tone are played simultaneously, we hear 556-552, or 4 beats per second. The beat frequency is 4 Hz. Uses ~ Piano Tuning