What is a mechanical wave?
- A disturbance transmitted by a medium from one point to another, without the medium itself being transported.
Transverse Traveling WavesEdit
What two factors determine the displacement of a particular point?
- x & t. x is where on the wave I am looking, and t is when.
What is a traverse wave?
- A wave where the direction in which the medium oscillates is perpendicular to the direction in which the waves propagate.
Define crests, troughs, wavelength, amplitude, period, and frequency. (Along with algebraic abbreviation)
- Crests = points where the vertical displacement above the horizontal is greatest.
- Troughs = points where the vertical displacement below the horizontal is greatest.
- Wavelength = λ = Distance between two crests/troughs.
- Amplitude = A = max displacement from the horizontal equilibrium position of the medium.
- Period = T = time to complete 1 cycle
- Frequency = f = 1/T
What are the four most important characteristics of a wave?
- λ, f, A, T
What is the most basic equation in wave theory?
- λ = vT
- λ(1/T) = v
- λf = v
Wave Speed on a Stretched StringEdit
What does wave speed depend upon? What is the equation?
- Wave speed depends on only physical characteristics of the string: tension and linear density.
- v = sqrt(FT/µ); µ = mass/length
What is constant when a wave changes medium?
The Mathematical Description of a Traveling WaveEdit
What is the basic mathematical form of a wave?
- y(x,t) = A*sin(ωt±κx); ±=direction. - = moving in positive x direction, + = moving in negative x direction
What is A, ω, and κ?
- A = Amplitude
- ω = angular frequency = 2πf
- κ = angular wave number = 2πk = 2π(1/λ)
Superposition of WavesEdit
What is superposition?
- Superposition is the interference of two waves. When then they cross, the resultant wave is the algebraic sum of the displacements of both waves.
What is "in phase" vs "out of phase"?
- In phase = crest meets crest
- Out of phase = crest meets trough
What is a standing wave? What are the physical properties?
- A standing wave is the superposition of two waves.
- A node does not move, so it's always 0 displacement. An antinode always moves the most, so on the crests/troughs.
What is the equation for harmonic/resonance wavelength? Frequency?
- Derived through pic. 1st harmonic: L = (1/2)λ, n=1. So algebra and get...
- λn = 2L/n; f = nv/2L
What is the fundamental standing wave/frequency? What is its relationship to other harmonics?
- Fundamental frequency is n=1, so f1 = v/2L.
- Harmonics: fn = nf1
What is the difference between closed-closed & closed-open?
- closed-closed can have all harmonics. 2L/n, must have nodes on both ends.
- closed-open can be only odd harmonics. 4L/n, must have node on closed, and antinode on open.
What are sound waves?
- Longditudinal waves composed of compressions and rarefactions.
What does the speed of a sound wave depend on? What is the equation?
- The medium it travels through. Particularly ρ (density) and B (bulk modulus).
- A low B = easily compressed.
- v = sqrt(B/ρ)
What is the measurement of the energy that a sound wave transmits?
- Intensity, I = energy/area.
What is the measurement of loudness level?
- dB. β = 10*log(I/I0)
What is a beat?
- A beat is the superposition of two waves that are close in frequency.
- The interfere constructively and destructively and go back and forth. This creates an "in-and-out" sound.
- Each time the waves begin to interfere constructively, increasing the sound level, a beat has occurred.
What is the formula for beat frequency?
- fbeat = |f1-f2|
Resonance for Sound WavesEdit
What are the qualities of a standing sound wave? (open-open and open-closed)
- Similar to the properties of a standing traverse wave.
- Open-open = both ends are antinodes. All overtones. 2L/n.
- Open-closed = antinode on open, node on closed. Only odd overtones. 4L/n.
The Doppler EffectEdit
What is the basis of the Doppler Effect?
- Relative movement between the source and detector creates compression or stretching of sound waves, changing their wavelength, and therefore their frequency.
What is the equation for the Doppler Effect?
- fD = (v±vD)/(v±vs)*fs.
- v = speed of sound.
- vD = speed of detector.
- vs = speed of the source.
- signs = direction.
How do you know which sign to use in the equation?
- Choose the signs based on logic. If they are moving away from each other, then the frequency should go down, so choose the signs that will make that happen.
If both the detector and source are moving, does that always induce a Doppler Effect?
- There must be RELATIVE MOTION.
The Doppler Effect for LightEdit
What is the equation for the Doppler Effect for light?
- λD = (1±u/c)*λs; assumption that u<<c.
What does it mean to be "red-shifted" as opposed to "blue-shifted"?
- That's a reference to whether a galaxy is moving towards or away from us. Blue has a longer wavelength than red, (ROYGBV), so a galaxy moving away from us has a bluish tint. Moving towards us has reddish tint.