3_3LabAssignment

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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 Tension Frequency f (Hz) Wavelength λ (cm) Wave Speed v (cm/s) Low 1.00 0.8571 0.8571. Low 1.25 0.9833 1.2291 Medium 1.50 2.0667 3.1001 Medium 2.00 1.65 3.3 High 2.00 2.1 4.2 High 3.00 2.1 6.3 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. As the tension on the string increases, the speed of the wave x a decreases b stays the same c increases 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. Name the physical quantities the wave speed depends on for a wave on a string. There are two. The velocity of a wave propagating along a string is contingent upon two distinct physical quantities:

Frequency, denoted as "f," refers to the quantity of full oscillations or cycles of a wave that transpire inside a unit of time, namely one second. The unit of measurement for this quantity is hertz (Hz). The wavelength (λ) refers to the spatial extent between two successive locations in a wave that exhibit phase coherence, such as consecutive crests or troughs. Typically, the unit of measurement employed is either meters or centimeters. The equation provides a mathematical representation of the interdependence between wave speed, frequency, and wavelength. The equation for wave speed (v) can be expressed as the product of frequency (f) and wavelength (λ). Part 2 Doppler Effect Open the simulation link labeled “Physics Aviary Doppler Effect Simulation. https://www.thephysicsaviary.com/Physics/Programs/Labs/DopplerLab/ Student Object Speed m/s Wave Speed m/s Frequency Hz Baca, Jacob 0 then 100 150 4.0 Bltom, Biniam 0 then 98 145 3.9 Brion, Matthew 0 then 96 140 3.8 Clevenger, Christopher 0 then 94 135 3.7 Eldridge, Marcus 0 then 92 130 3.6 Higgins, Sean 0 then 90 125 3.5 High, Parker 0 then 88 120 3.4 Jimenez, Serena 0 then 86 115 3.3 Mejia, JeffreyLousie 0 then 84 110 3.2 Mohibi, Hasibullah 0 then 82 105 3.1 Poor, Travis 0 then 80 100 3.0 Powell, Anniya 0 then 78 150 4.0 Smith, Shawn 0 then 76 145 3.9 Tanner, Anthony 0 then 74 140 3.8 0 then 72 135 3.7 0 then 70 130 3.6 0 then 68 125 3.5 0 then 66 120 3.4 0 then 64 115 3.3 0 then 62 110 3.2 0 then 60 105 3.1 Instructor 0 then 58 100 3.0

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Start by setting the object speed to zero . Set the Wave Speed and Frequency to the values listed by your name in the table. Click start and observe the wave fronts depicted in the simulation moving away from the source at the wave speed. Pause the simulation to measure the wavelength by noting the squares in the grid between one wave front and the next. Use the method described in part 1 to get precise wavelength measurements. 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 70 m/s 1.0 Hz 75 Substitute your frequency and wavelength into the equation below to calculate the wave speed. Given the frequency (f) is equal to 1.0 Hz. The wavelength (λ) is equal to 75 centimeters. The equation for wave speed (v) can be expressed as the product of frequency (f) and wavelength (λ). The speed of a wave (v) can be calculated by multiplying the frequency (1.0 Hz) by the wavelength (75 cm), resulting in a wave speed of 75 cm/s. 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. Frequency λ in front λ behind 3.9 10m 60m 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 Perceived Frequency (ahead) = Actual Perceived Frequency (ahead) = 3.9 Hz × 145 m/s / 243

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Frequency × Speed of Wave / (Speed of Wave + Speed of Source) m/s Perceived Frequency (ahead) ≈ 2.318 Hz Perceived Frequency (behind) = Actual Frequency × Speed of Wave / (Speed of Wave - Speed of Source) Perceived Frequency (behind) = 3.9 Hz × 145 m/s / 47 m/s Perceived Frequency (behind) ≈ 12.027 Hz 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. Student Source velocity, m/s Baca, Jacob 333 Bltom, Biniam 329 Brion, Matthew 326 Clevenger, Christopher 322 Eldridge, Marcus 319 Higgins, Sean 316 High, Parker 312 Jimenez, Serena 309 Mejia, JeffreyLousie 306 Mohibi, Hasibullah 303 Poor, Travis 300 Powell, Anniya 297 Smith, Shawn 294 Tanner, Anthony 291 Baca, Jacob 288 285 282 279 276 273 270 Instructor 267

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 329 m/s Source Frequency f 343 Hz Source Wavelength λ 1m

Speed of Sound 343 mls Source Approaching Observer Source Receding from Observer perceived freq perceived wavelength perceived freq perceived wavelenght 8403.5 Hz 0.04m 175.07 Hz 1.98m 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 ( v s ) and the speed of the source ( v ) . Equation with values substituted Result f a = f v s /(v s –v) = (343) (343) /[(343)–(329)] 8403.5 Hz f r = f v s /(v s +v) = (343) (343) /[(343)+(329)] 175.07 Hz 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 329 m/s v = v s (f a -f)/f a = (343 m/s) [( 343) – (175.07 Hz )] / (175.07 ) 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 329 m/s v = v s (f-f r )/f r = (343 m/s) [ (175.07Hz) – (343 Hz )]

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/ (175.07 ) 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 =v= c*(f-f r )/f r 3.5 x10^7 m/s

3_3LabAssignment

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