Waves at Media Boundaries

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

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