Waves at Boundaries.

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Presentation transcript:

Waves at Boundaries

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?

Free End Reflection

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

Fixed End Reflection

Fixed End Reflection

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

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

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

Nodes and Antinodes

Fundamental Frequency and Harmonics

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

Standing Wave: One fixed, one free end Antinode Node

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

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

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

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

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= 0.22 m 2.2 m 0.25 m

Your Turn… MHR pg. 352 # 1-7