
What is the linear wave equation?

The linear wave equation applies (restate) in general to various types of ________ waves. y represents various positions. What does it represent:
For a string
For a sound wave
For EM waves
 traveling waves


Wave Motion on a String
The string is under tension T. Consider one small string element of length Ds. State the formula (3) for the net force acting in the y direction:
F _{r} =

The formula for net force acting in the y direction (restate) uses the ______ ______ approximation. What is the formula for m, Δs, v (the wave speed of the wave), μ and t(time)
 small angle approximation
 μ:
 m = ρv = ρAL_{(length)}
 μ = m/L = ρV = ρA_{(Area)}_{}
 t = L/v
 **1) T is for tension and 2) If dealing with diameter, represent radius as d/2


State an example of a twodimensional wave and a threedimensional wave
 Twodimensional wave: circular wave such as ocean waves
 Threedimensional wave: spherical waves such as waves emit from loudspeakers and lightbulbs

Wave fronts are the _____ of the wave. They are spaced ______ wavelength(s) apart. The circular wave fronts move ______ from the source at speed v. Very far away from the source, small sections of the wave fronts appear to be ______ lines
 crests
 one wavelength
 outward
 straight

What is the phase of the wave Φ?
What is the formula for phase difference ΔΦ? (6)
 Phase of the wave Φ = (kx  ωt + Φ_{0})

Phase difference between two points on a wave depends on only the ratio of their separation Δx to the _________, (__).
wavelength, (λ)

 Minimum is 0 so it can't be c or d
 The answer is (b) because we are plotting time, we will start from the specified point and ask does the pulse affect this point (considering the direction)
 **If this was left, the answer would be flat at the taxis
 2nd explanation:
 The point is at rest before and after the wave passes through it, and when wave reaches there it suddenly moves upwards (to emulate the part of the wave that hits it first) and then slowly moves downwards till the wave goes. This is shown in B.
 **If this was left, the answer would be flat at the taxis


 v = (Δx_{distance}/Δt_{time}) = λf = λ /T = (√T/μ)
 1st graph:
 λ = 0.6m
 2nd graph:
 T = 0.2s
 v = λ/T = (0.6m/0.2s)
 B.) v = 3.0 m/s

Sound waves in gases and liquids are always ________ waves, but sound waves in solids can be either _________ or ________. They travel through any ______ ______ (give 3 examples).
 longitudinal waves
 longitudinal or transverse
 material medium (including solid, liquid, and gas states)

Longitudinal sound waves can be construed as _______ waves, they comprise of ____ (_______) and _____ (_________) pressure regions
 pressure waves
 high (compression) and low (rarefactions)

The loudspeaker cone moves back and forth creating regions of ______ and _______ pressure aka ________ and ________. The sound wave is a ________ wave. Compressions are ______ and rarefactions are _______.
 higher and lower
 compressions and rarefactions
 pressure wave
 crests
 troughs


A sound wave may be considered either a _______ wave or a _______ wave. The pressure wave is _____ out of phase with the displacement
 displacement wave
 pressure wave
 90°

The mathematical description of sinusoidal sound waves is very similar to sinusoidal waves on a string. State the formula for displacement of a small element in both right and left direction. Explain the components of the equations

The variation ΔP in the pressure of the gas as measured from its equilibrium value is also sinusoidal. What is the formula ΔP (moving in either direction)?
Define DP_{max}

The pressure amplitude is proportional to the ________ amplitude. State the proportionality (and explain each component):
ΔP_{max} =
 displacement amplitude

The speed of the wave depends on the properties of the _______. Its speed depends on 2 things, name them
 medium
 1) The medium's resistance to compression (or deformation of the medium)
 2) Density of the medium

The greater the resistance to compression, the _______ the sound will travel in the medium. The greater the density of the medium, the _______ sound will travel. In general, sound travels _______ through gases, then liquids, and _______ through solids
 faster
 slower
 slowest
 fastest

The speed of sound waves depends on the properties of the _______. Sound waves in air depends on ________. State the formula for velocity or speed of a sound wave and explain the component.
Finally what is the speed of sound in air at 20°C?
 medium
 temperature

State two kinds of speed or velocity. Explain both and state their formula for one
Which is is constant in a uniform medium

Define Light waves
Being selfsustaining means it requires no _____ ______. All electromagnetic waves travel through a vacuum with the same ______. What is this value called and what is its numerical value?
 Light waves: a selfsustaining oscillation of the electromagnetic field
 material medium
 speed
 v_{light} = c = 299792458 m/s

Various types of electromagnetic (EM) waves make up the _____ ______. There is no sharp division between one kind of _____ wave and the next. There are overlaps between types of waves. Visible light is a small portion of the _______. Types are distinguished by ________ or ________. Frequency ________, as wavelength ________
 EM spectrum
 EM wave
 spectrum
 frequency or wavelength
 increases
 decreases

Adjacent wave types exhibit some _______ of frequencies. Explain or give examples:
 overlap

Part of the spectrum detected by the human eye are from _____ nm to _____ nm. Different wavelengths correspond to different ________. State the range
 400 nm
 700 nm
 colors
 The range is from red (I~ 7*10^{7} m) to violet (I~4*10^{7}m)

Light waves travel with speed c in a _______, but they slow down as they pass through transparent materials. The speed of light in a material is characterized by the material's _______ ____ _______, (__)
 vacuum
 index of refraction, (n)

What is the formula for index of refraction (2)
What are the implications if we are in a vacuum or in another medium?

State the TWO BIG RULES for Waves

The speed of a wave is determined by the type of ______ and the characteristics of the _______, not by the _________. This applies to different waves in one _______. For instance, sound and light both travel in air, but at different _______. Since v = _____, and the wave speed does NOT depend on _______, thus, if frequency changes, it only affects the _______ and not _____ _____
 wave
 medium
 frequency
 medium
 speed
 v = λf
 frequency
 wavelength λ
 wave speed, v

When a wave passes into another medium, its speed _______, but its frequency ______ _____. Frequency of a wave is the _________ of the source. Similar to continuity equation: rate in = _____ _____. Applies to a single wave in different _______. In different medium, the wave speed ______. Since v = ____, thus wave will undergo a different wavelength in _______ medium
 changes
 does not
 frequency
 rate in = rate out
 media
 changes
 v = λf
 different

