## IntroEdit

**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(F
_{T}/µ); µ = mass/length

**What is constant when a wave changes medium?**

- Frequency

### 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

## Standing WavesEdit

**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...
- λ
_{n}= 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 f
_{1}= v/2L. - Harmonics: f
_{n}= nf_{1 }

**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.

## Sound WavesEdit

**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)

### Sound LevelEdit

**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/I
_{0})

### BeatsEdit

**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?**

- f
_{beat}= |f_{1}-f_{2}|

## 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?**

- f
_{D}= (v±v_{D})/(v±v_{s})*f_{s}. - v = speed of sound.
- v
_{D}= speed of detector. - v
_{s}= 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?**

- λ
_{D}= (1±u/c)*λ_{s}; 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.