This post includes a video showing single slit diffraction of a LASER beam. The derivation develps formulas to find the diffraction maxima and minima as a function of angle. Continue reading Diffraction

# Category Archives: Physics Unit 12: Waves

# deciBells Beats and Doppler

Beats:

WHAT YOU NEED TO KNOW:

fbeat = | fA – fB|

# Standing Waves in Tubes

# 4 Kinds of Waves

Transverse waves are the easiest to picture, because syou can visualize and often see material moving. Essential knowledge: Transverse, Longitudinal, Torsional and Love Waves. Continue reading 4 Kinds of Waves

# The Doppler Effect – formulas

**Lesson Objective:** How to calculate the Doppler Effect for moving sources and detectors. How to solve the Doppler equation for the speed of a galaxy based on its Red or Blue shift.

**Warm Up:** {FM} Why is the Doppler Shift formula for light different than the Doppler Shift formula for sound?

What you need to know:

Review:

For Sound: fd = fs (v-vd) / (v-vs)

Derive expressions for fd where vd=0 and where vbs=0 (see pg 415).

New material:

For light: f observer = f (1 +/- v/c) for v<<c

And the “red shift” DL =Lobserved – L = +/-(v/c) L

Where D means delta and L means Lambda.

Do Practice Problems pg 456 # 16-19, you will be called on to present your work at the board.

Relativistic Doppler Effect: Now the problem is that the speed of light is a constant and we are stuck never being able to exceed the speed of light.

Q: What is the speed of light in m/s? in miles/sec?

One of Einstein’s colleagues, Lorenz, came up with a transformation that allowed one to create mapping between points in space-time. Using the Lorentz transformation, they derived the relativistic Doppler Effect:

nu’ = nu [ (1-v/c) / (1+v/c) ]^1/2

This is the Relativistic Doppler Effect which applies when v gets close to c.

This post from Wikipedia has the derivation of this equation – but it’s really complicated. Diagrams 1 and 2 will give you the general idea.

The Relativistic Doppler Effect

Now calculate the non-relativistic and relativistic Doppler “Red Shifts” for a star moving away from you at;

v=0.9c

v=0.99c

v=0.999c

Assume the star emits 500nm light.

Include your results in a table and in the third column, calculate the % difference between the non-relativistic and the relativistic Doppler red shifts.

Exit Assessment: What would 500nm light look like of you were traveling faster than the speed of light?

# Physics Unit 12: Waves and Harmonic Motion

Intro to sound ad waves. Covers amplitude, wavelength, frequency, wave velocity. Includes CA std. Includes Electra Spectra video, phet wave simulator and lightning sound delay. Continue reading Physics Unit 12: Waves and Harmonic Motion