3.3 Lab Assignment: Waves

3.3 Lab Assignment: Waves

Part 1: Wavelength, Frequency, and Wave Speed

Open the simulation “Wave on a String” by clicking on the link in Canvas.  Or hold the control [ctrl] key down and click on this link: https://phet.colorado.edu/en/simulation/wave-on-a-string

Pause the simulation.

Set the controls to Oscillate and No End (top left and right).

Set the amplitude to 0.75 cm. 

Set the frequency to 1.00 Hz

Set the Tension to Low.

Set the Damping to zero.

Click the box to show the rulers.  Note the rulers mark centimeters (cm).

Click play and observe the wave. 

To measure the wavelength, click pause.

One wavelength is the distance to the next peak.  In the below example, the wavelength is 1.1 cm (blue double arrow).  This is not very precise, however. 

For better precision, position the horizontal ruler so that the 0.0 cm mark is over the left-most peak. Measure L to the right-most peak (purple arrow). 

L = 6.40 cm

Then divide by the number of gaps between these end peaks. (Green numbers)

n = 6

λ = L/n = 6.40 cm/6 = 1.07 cm 

This is the most accurate way to get precise measurement of the wavelength.  Use it here and in part 2.

Make sure damping is set to zero and the no end and oscillate options are set.  Start with tension on low.

Set the frequency and wave tension to the following values. Let the wave fill the screen.  Measure the wavelength and calculate the wave speed.

Formula: Wave Speed = (frequency)(Wavelength) = f λ

Note: as presented in class, when you change the frequency of the wave but not the physical properties of the medium, the speed should not change.  So, you should get approximately the same speed for each Tension setting in the above set of measurements.  The simulation is capable of very high levels of accuracy, so if your wave speed varies by more than a few percent for the same tension setting, review your wavelength measurements to see if one of them is in error.

For confirmation, look at the textbook Chapter 6, section 1 for a formula that can allow one to measure the wave speed of a wave on a string.

Part 2 Doppler Effect 

Open the simulation link labeled “Physics Aviary Doppler Effect Simulation. https://www.thephysicsaviary.com/Physics/Programs/Labs/DopplerLab/

Start by setting the object speed to zero.  Set the Wave Speed and Frequency to the values listed by your name in the table. 

Make a screen shot of your wave. Be sure the screen shot is big enough to fill the full width of the document. 

Paste Screenshot here.

Double check that you set the object speed to zero for this part.

Put your wave speed, frequency, and wavelength in the table below.

Wave Speed	Frequency		Wavelength
Substitute your frequency and wavelength into the equation below to calculate the wave speed.

Click “End” and set your object speed to the non-zero value listed by your name in the table on page 3.  Keep your wave speed and frequency the same as before.

Click “Start”.  Observe the simulation and pause it when you can measure the wavelength in front and behind the source.

Make a screen shot of your simulation and paste it below.  Be sure the screenshot is big enough to fill the full width of the document. 

Paste Screenshot here.

Record the two wavelengths and the frequency of the source.

Use the formula for frequency to calculate the frequency in front of and behind the moving source.  Note: v stands for the speed of the wave, not the speed of the source.

Formula	Perceived Frequency

This should show a higher frequency perceived ahead of the source and a lower frequency behind the source.

Part 3 Doppler Effect, advanced

Open the OPhysics Doppler Effect Simulation. See link in the assignment.

https://ophysics.com/w11.html

Adjust the source velocity to the value listed by your name in the table below. Click and drag the slider to get as close as you can to your assigned number.  Then click to the right of the slider circle to adjust the speed up 1 m/s or click to the left of the slider circle to lower the speed 1 m/s.

Click Start and while the source is approaching the observer, record the perceived frequency and wavelength.  Click Reset and Start as needed until you have recorded your values.

Then click Start again and wait for the source to pass the observer.   Record the perceived frequency and wavelength again.

Table begins on the next page.

Source Velocity, v
Source Frequency f
Source Wavelength λ
Speed of Sound
Source Approaching Observer			Source Receding from Observer
perceived	perceived		perceived	perceived

Use the values to verify the following formulas. Use the Source Frequency for f and the source velocity for v.  These allow you to predict the frequency shift if you know the speed of sound (vs) and the speed of the source (v).

Equation with values substituted	Result
fa = f vs/(vs–v) = () () /[()–()]
fr = f vs/(vs+v) = () () /[()+()]

Fill in one of the two options for showing your substituted values and units.  You do not need to fill in both equations.  The second is just for those who have problems with the equation formatted by the Word Equation tool.

If you know the speed of sound, the frequency of the source and the apparent frequency when the source is approaching, you can solve the first equation and calculate the source velocity.  A version of this is used with a radar gun to calculate the speed of a car as it approaches the radar gun.

Equation with values substituted	Result
v = vs (fa-f)/fa = (343 m/s) [( ) – (343 Hz )] / ( )

Substitute your values for the apparent frequency when the source is approaching the observer to calculate the source velocity. 

Substitute your values in the top formula, unless your version of Word does not support the equation tool, in which case use the text line version below it.

If the source is moving away from the observer, use the following formula to calculate the source velocity from the observed frequency when the source is moving away from the observer.

Equation with values substituted	Result
v = vs (f-fr)/fr = (343 m/s) [(343 Hz) – ( )] / ( )

As a final exercise use the following data from measurements of starlight from a galaxy to determine the frequency shift due to the Doppler Effect.

The galaxy looks like this:

A particular frequency marker common in all starlight is due to quantum mechanical effects and has a frequency of 691.6 THz.

That frequency marker in the starlight from this galaxy has a frequency of 627.6 THz.  As this is a lower frequency, that indicates the galaxy is receding from earth (called a red shift, because it moves toward the red end of the color spectrum).

The speed of light is known to be 300,000,000 m/s. It is usually represented by the letter c. 

Substitute these into the formula used above to get the speed at which this galaxy is moving relative to earth.

Formula	Galaxy Speed
=