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Mind Map by Kieran Lancaster, updated more than 1 year ago
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Created by Kieran Lancaster
over 6 years ago
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Chapter 12 - Waves 2
- Superposition of
Waves
- Overlap of two waves at a point in space
- Resultant displacement is the sum of
displacements of the original two waves
- Resultant displacement is the sum of
displacements of the original two waves
- Constructive interference - Two waves in phase create a
resultant wave with increased amplitude
- Destructive interference - Two waves in antiphase create a
resultant wave with decreased or zero amplitude
- Overlap of two waves at a point in space
- Interference
- Coherence - Waves emmitted from two sources with
constant phase difference and frequency
- Maxima - Loud spots created from waves arriving in phase,
constructively interfering. Path difference of whole number of
wavelengths (0, λ, 2λ)
- Minima - Quiet spots from waves arriving in antiphase,
destructively interfering. Path difference of half number of odd
wavelengths (0.5λ, 3/2λ, 5/2λ)
- A signal generator with two speakers can be
used to create an interference pattern, dected
by a microphone
- A microwave source can be used along with double slits, to
create an interference pattern detected with a receiver
- Coherence - Waves emmitted from two sources with
constant phase difference and frequency
- Young double slit
experiment
- It demonstrates the wave nature of monochromatic light. The slits have to be
narrow enough to diffract the light, which creates an interference pattern in the
form of light and dark fringes
- Seperation between slits = d
- Difference between screen and slits is L, where L>>d
- Two bright fringes observed at P and C, with separation between them of y
- Path difference s = λ, since L>>d
- The two dashed rays of light are almost parallel
- Sinθ₁ = sinθ₂ = tanθ₂
- Where Sinθ₁ = s/a and tanθ₂=x/L (s=λ)
- Therefore λ/a = x/L
- (In the formula book, distance to screen L is represented by D)
- It demonstrates the wave nature of monochromatic light. The slits have to be
narrow enough to diffract the light, which creates an interference pattern in the
form of light and dark fringes
- Stationary
Waves
- Formed when two progressive waves travelling in
opposite directions with the same frequency, superpose
- When the two waves are in antiphase, they create a
node, where displacement is always zero.
- When the two waves are in phase, an antinode is
formed, where amplitude and intensity is greatest
- In a stationary wave, the seperation
between two nodes/antinodes is 1/2λ.
The stationary wave has the same
frequency, but doesn't transfer energy
- By reflecting microwaves off a metal sheet, a
stationary wave can be formed. The wavelength
can be detected by moving a receiver, until it
detects nodes and antinode. The distance between
successive nodes is λ/2, λ being wavelength of the
microwaves
- Formed when two progressive waves travelling in
opposite directions with the same frequency, superpose
- Harmonics
- Fundamental frequency - minimum frequency of a stationary wave needed to
create half a wavelength (depending on string's mass, tension and length)
- Harmonics are produced, increasing in integer multiples of F₀
- V=fλ shows that as frequency increases, wavelength decreases.
This is because at a fixed tension, v remains constant
- This wave can be created with a vibration generator, using a string attached to a fixed point
- Fundamental frequency - minimum frequency of a stationary wave needed to
create half a wavelength (depending on string's mass, tension and length)
- Stationary waves in air
columns
- In a tube closed at one end, there is an antinode at the open end, the
closed end is a node, . Harmonics increase by 1/2λ e.g 1/4λ , 3/4λ, 5/4λ.
The harmonics are always in odd multiples of the fundamental
frequency, 3F₀, 5F₀ etc.
- In an open tube, there are antinodes at both ends, and harmonics
increase by 1/2λ, e.g 1/2λ, λ, 3/2λ. Harmonics are all integer multiples
of F₀, 2F₀, 3F₀ etc.
- A tuning fork can be used to create a stationary wave
in a resonance tube. If f (tuning fork) matches F₀, the
sound gets louder and resonates.
- The length of tube above the water must be L=1/4λ.
The speed of sound can be calculated with v=fλ =f*4L
- In a tube closed at one end, there is an antinode at the open end, the
closed end is a node, . Harmonics increase by 1/2λ e.g 1/4λ , 3/4λ, 5/4λ.
The harmonics are always in odd multiples of the fundamental
frequency, 3F₀, 5F₀ etc.
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