Standing Waves Waves and Sound

Phase Wave alignment In phase: Two waves are in phase when their wavelengths are the same and their crests align perfectly (amplitudes do not have to be the same). Out of phase: Wavelengths differ and/or crests do not line up. 180o out of phase: Wavelengths are the same, but crests line up with troughs.

Interference / Superposition Addition of two or more waves Constructive Interference: When waves add to create a larger wave. The greatest constructive interference occurs when waves meet in phase. When these waves meet they create one wave that is twice as large. Destructive Interference: When waves add to create a smaller wave, or no wave at all. The greatest destructive interference occurs when waves meet 180o out of phase. These ways destroy each other. At the instant they meet they cancel.

Standing Wave When waves reach a boundary they reflect (bounce back). Incident wave: The inbound wave. Click to see this wave develop in the diagram below. If the inbound waves hits the boundary, as shown below, then the reflected waves will match the incoming waves perfectly. Reflected wave: The wave bouncing off the boundary. Click to see it form. While the resulting wave pattern oscillates it does not appear not to move right or left. It appears to the standing still. Nodes: points that do not appear to move. Antinodes: points that vibrate the greatest. Antinode Node

Standing Wave How many wavelengths are present in this standing wave? 1 1 0.5 2.5 wavelengths These diagrams depict commonly encountered fractions of standing waves. 1 0.75 0.5 0.25

Strings In musical string instruments the vibrating strings are tied down at each end. When they are set in motion they vibrate forming standing waves. Several wave forms can be created in a string with a fixed length L . L mode L λ v 1st Harmonic 2nd Harmonic 3rd Harmonic For strings multiples of half wavelengths create standing waves.

Example 1 A string tied between two points is vibrating at its fundamental frequency. The speed of the waves in the string is 750 m/s and its frequency is 500 Hz. Determine the length of the string. The fundamental frequency f0 is the simplest wave form that forms a standing wave in a string. For vibrating strings a half a wavelength creates the fundamental. If half a wavelength fits in the length L of the string, then Substitute this into the equation for wave speed. Substitute values and solve. Strings do not use the speed of sound in air. The medium is the string, not air. While a vibrating string will cause the air around it to vibrate, the speed of the vibrating string is different than the speed of sound in air. When working with strings use the speed of the vibrating string.