1. Waves at Boundaries

2. What is a boundary? A boundary is also known as a medium.
A medium or media is a material that allows a wave to pass through
Examples of mediums:
Air, water, wood, steel
What about a vacuum? Can a sound wave travel through a vacuum?

3. Free End Reflection

4. Free End Reflection
A reflection that occurs when the medium is not fixed at one end
The amplitude of the incoming pulse is equal to the amplitude of the outgoing pulse

5. Fixed End Reflection

6. Fixed End Reflection

7. Fixed End Reflection
When the medium is fixed at one or both ends, the amplitude of the incoming pulse is equal but opposite of the outgoing pulse

8. Standing Wave The incoming and reflecting waves interfere
They create a wave pattern that appears to be stationary

9. Standing Waves Standing waves create: NODES and ANITNODES
Nodes: the particles of the medium are at rest
Antinodes: the particles of the medium are moving with greatest speed ; the amplitude is twice the amplitude of the original wave

10. Nodes and Antinodes

11. Fundamental Frequency and Harmonics

12. Standing Waves: Two open ends- free ends
This wave is common with brass instruments i.e. trumpets
Antinode
Antinode

13. Standing Wave: One fixed, one free end
Antinode
Node

14. Calculations with Standing Waves Part One
Media with fixed ends or free ends ( ie guitar, clarinet, flute, etc)
Ln = nλ/2
Where:
Ln = length of the medium or string
n= number of harmonics ie 1,2, 3 etc.
λ= wavelength

15. Calculations with Standing Waves Part Two
Media with fixed end and free end i.e. trumpet with a mute attached to it
Ln = (2n-1)λ/4
Where:
Ln = length of the medium or string
n= number of harmonics ie 1,2, 3 etc.
λ= wavelength

16. Let’s Solve some problems…
The speed of a wave on a string with a fixed end and a free end is 350 m/s. The frequency of the wave is 200 Hz. What length of string is necessary to produce a standing wave with the first harmonic?
Answer:
L1 = 0.44m

17. Problem #2:Guitar String
The 6th harmonic of a 65 cm guitar string is heard. If the speed of the sound in the string is 206 m/s, what is the frequency of the standing wave?
Answer:
f6 = 950 Hz

18. Problem #3: Rope
A 0.44 m length of rope has one fixed end and one free end. A wave moves along the rope at the speed of 350 m/s with a frequency of 200 Hz at n=1.
What is L1 if the frequency is doubled?
What is the length of the string if n=3?
What is L1 if the speed of the wave on the string is reduced to 200 m/s?
Answers:
L1= m
2.2 m
0.25 m

19. Your Turn…
MHR pg. 352 # 1-7