1. Superposition & Standing waves
Chapter 14
Superposition &
Standing waves

2. 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.

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

4. 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

5. 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

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

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

8. Standing Waves in Strings

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

10. 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.

11. 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

12. Beats: Interference in Time

13. That is all for the semester!
Thank you!