Physics B

Anatomy of a wave…

Waves
• https://www.youtube.com/watch?v=2awbKQ2DLRE

Determine: λ, A, T, f, v, k, and ω

Period (T): how long it takes for a single wave to pass a single point.
seconds
Frequency (f): number of waves that pass a given point in a time period of one second.
Hertz (Hz) = 1/s
Q. What is the period of a 60 Hz wave traveling at 3.0 x 10 8 m/s?

𝑣 = 𝑓λ
This equation gives us the speed of a wave, given the information we know about a wave….. This will be VERY important later on.
Q. If the speed is a constant (depending on the wave), what does this tell us about the relationship between the frequency and the wavelength?

k (wave number)
2𝜋 𝑘 =
λ
The distance between consecutive maxima.

ω (angular frequency)
ω = 2𝜋𝑓 = 𝑣𝑘
Angular frequency = 2π*frequency or speed of wave * wave number
ω = [rad/sec] http://www.animatedscience.co.uk/blog/wpcontent/uploads/focus_waves/auxcircle.html

Φ (Phase Shift) is the fraction of the wave cycle which has elapsed relative to the origin.
In phase Out of Phase

Together we get…. The mathematical description of a wave!
𝑦 𝑥, 𝑡 = 𝐴𝑐𝑜𝑠(𝑘𝑥 − ω𝑡 + ϕ)
A sinusoidal wave moving in the +x direction
But, we will work primarily with the simpler version: 𝑦 𝑡 = 𝐴𝑐𝑜𝑠 𝑤𝑡

Wave traveling left or right?
𝑦 𝑥, 𝑡 = −𝐴𝑐𝑜𝑠 𝑘𝑥 + 𝑤𝑡
Incident wave traveling to the left 𝑦 𝑥, 𝑡 = 𝐴𝑐𝑜𝑠 𝑘𝑥 − 𝑤𝑡
Incident wave traveling to the right

Sine and Cosine Waves

Sine and Cosine Waves continued…
• To determine nodes, all you need to do is know about the individual types of waves, sine and cosine.
• For sine, the function is 0, when the inside of the function is:
0, π, 2π, etc…
• For cosine, the function is 0, when the inside of the function is: 𝜋
2
,
3𝜋
2
, etc…

Practice http://www.cabrillo.edu/~jmccullough/Physics/Waves_Sound.html

What does the full 𝑦 𝑥, 𝑡 = 𝐴𝑐𝑜𝑠(𝑘𝑥 − ω𝑡 + ϕ) equation look like?

So, why do we need to know this?
𝑜

Superposition

Bell Work: What do EM waves look like?
The EM Wave http://www.cabrillo.edu/~jmccullough/Applets/Flash/Optics/EMWave.swf

Covered
• Wave Characteristics
• The Wave Equation
• Interference &
Superposition
• Causes of EM Waves
• Electromagnetic
Spectrum
• Characteristics of
Particular EM Waves
Today
• The E & M in EM Wave
• Speed of Light
• Energy of EM Waves
• Doppler Shift

Oscillating Electric & Magnetic Fields
Where, c is the speed of light!
𝑐 = 3 × 10 8 m/s
Q. So……. What causes this to even happen?

Oscillating CHARGED Particles http://phet.colorado.edu/en/simulation/radio-waves

The EM Spectrum
Because of the large variation in EM waves (massive differences in wavelengths and frequencies), we separate them into categories…
Radio
Microwave
Infrared
Visible
Ultra Violet
X-Ray
Gamma

The Speed of Light 𝑐 = 3 × 10 8 m/s
Measuring the Speed of Light https://www.youtube.com/watch?v=DMKE5YGLnmc
Breaking the Speed of Light https://www.youtube.com/watch?v=EPsG8td7C5k
Speed of an EM Wave 𝑐
Speed of Light = wave length * frequency

Energy of an EM Wave
Energy = Constant * frequency

The Doppler Effect http://www.cabrillo.edu/~jmccullough/Applets/Flash/Fluids,%20Oscilla tions%20and%20Waves/DopplerWaveFronts.swf
Applications?
Photonic Boom?