Superposition & Standing waves Chapter 14 Superposition & Standing waves

The Principle of Superposition If two or more traveling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of individual waves. Two traveling waves can pass through each other without being destroyed or even altered.

Interference of Waves Two waves traveling to the right According to the principle of superposition, the resultant wave is: Amplitude Phase angle

Interference of Waves In phase f=0, constructive interference Some source of disturbance; A medium; Some physical mechanism through which particles of the medium can influence one another. In phase f=0, constructive interference Out of phase f=p, destructive interference Other phase f=p/3, y falls to somewhere between the extremes

Standing Waves Two waves, one traveling to the right and one to the left According to the principle of superposition, the resultant wave is: The function of a standing wave

Standing Waves In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.

Standing Waves in Strings The wavelength of the nth mode of vibration

Standing Waves in Strings

Standing Waves in Strings The fundamental frequency of vibration is adjusted by pressing and releasing the finger. The length of string is changed!

A two-dimensional standing wave on a disk the fundamental mode A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

Beats: Interference in Time The displacement that each wave produced at a fixed point According to the principle of superposition, the resultant displacement: Amplitude varies in time

Beats: Interference in Time

That is all for the semester! Thank you!