1. Waves at Media Boundaries
Section 9.2

2. Key Terms Media Boundary Free-end Reflection Fixed-end Reflection
Transmission
Standing Wave
Node
Antinode
Fundamental Frequency/First Harmonic
Harmonics
Overtone

3. Media Boundaries
Wave speed depends on the properties of the medium through which the wave is travelling.
All media have boundaries.
The location where two media meet.

4. Free-End Reflections
If a wave travels from a more dense medium to a less dense medium, it will travel more quickly in the more dense medium.
Wave moving towards the boundary will be reflected with the same orientation and amplitude

5. Fixed-End Reflection
As a wave moves towards a fixed boundary, it will reflect.
Reflected pulse has the same shape as the incoming pulse, but its orientation is inverted.

6. Amplitude
When a wave encounters a boundary that is not strictly free-end or fixed-end, the wave will split in two.
One wave is reflected
Energy “bounces back”.
The other is transmitted.
Energy passes into new medium.
Amplitude of the two waves may not be equal, but the sum of the amplitudes will be equal to that of the original wave.

7. Media Boundaries
Not all difference in media boundaries are as dramatic as fixed-end or free-end.
Water  Air
If a wave travels from a medium in which the speed is faster (more dense) to a medium in which the speed is slower (less dense), the wave particles can move more freely
Energy is transferred into new medium
Reflected wave has same orientation

8. Media Boundaries The opposite is also true.
Air  Water
If a wave travels from a medium in which the speed is slower (less dense) to a medium in which the speed is faster (more dense), the wave particles cannot move as freely
Energy is transferred into new medium
Reflected wave has inverted orientation

9. Standing Waves
Suppose a series of waves is sent down a string that is fixed at both ends.
At a certain frequency, reflected waves will superimpose on the stream of incoming waves to produce waves that appear stationary
The locations in which the particles of the medium do not move are nodes.
The locations in which the particles of the medium move with the greatest speed are antinodes.

10. Standing Wave

11. Standing Waves
Waves interfere according to principle of superposition.
Waves are moving continuously
At the antinodes, the amplitudes of the troughs and crests are double that of the original wave.
At the nodes, the amplitudes are the same but one is a crest and the other is a trough.
Interference pattern appears to be stationary because it is produced by otherwise identical waves travelling in opposite directions.

12. Standing Waves Between Two Fixed Ends
Standing waves can be predicted mathematically.
Consider a string with two fixed ends
Standing wave with nodes at both ends.
The shortest length of the string, L, is equal to one half of the wavelength.
The frequency of the wave that produces this simplest standing wave is called the fundamental frequency
First harmonic
All standing waves to follow require frequencies that are whole-number multiples of the fundamental frequency.
Additional standing wave frequencies are known as the nth harmonic of the fundamental frequency

13. Number of Nodes Between Ends
Symbol
Number of Nodes Between Ends
Diagram
Harmonic (n)
Overtone f0
First
Fundamental f1 1
Second f2 2
Third f 3
Fourth

14. Harmonics and Overtones
Harmonics consist of the fundamental frequency of a musical sound as well as the frequencies that are the whole-number multiples of the first harmonic.
When a string vibrates with more than one frequency, the resulting sounds are called overtones.
Similar to harmonics, however the first overtone is equal to the second harmonic.

15. Calculations with Standing Waves
The length of the medium is equal to the number of the harmonic times half the standing wave’s length.
For a media with a combination of fixed and free ends (node at one end and antinode at the other), the equation is:

19. Summary

20. Homework
Page 426
Questions 1-5