Standing Waves – Part 1 – Drawing Standing Waves
Equipment
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· Wave worksheet (found at end of this Exploration)
· Colored pencils (three different colors)
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Part One: The Properties of Waves
1. On the top graph of the wave worksheet, draw a wave that has an amplitude of 1 cm and a wavelength of 8 cm. Start the wave with a vertical displacement y = 0 cm at x = 0 cm. Draw this wave in pencil. When you are satisfied that you have drawn it correctly, draw over it with a colored pencil. This will be wave 1 and it will be considered to be moving to the right. Record your color choice in the legend. Using the same colored pencil as you used to draw the wave, indicate the direction of motion of the wave by an arrow on the graph. How far would this wave travel in one period of the wave? ______How do you know? ______
2. Using the same technique, and a second color, draw another wave on the same graph grid that is identical to wave 1 and aligned with wave 1 so that the peaks of wave 1 line up with the peaks of the new wave (draw it right on top!). This second wave will be wave 2, and it will be considered to be moving to the left. Record your color choice in the legend. Using the same colored pencil you used to draw wave 2, indicate the direction of motion of wave 2 by an arrow on the graph. How far would this wave travel in one period of the wave? ______How do you know? ______
3. When two or more waves are traveling together in the same medium, each wave will try to disturb the medium by the same amount it would if it was the only wave in that medium. That is, if one wave would cause a displacement of 5 cm at some point, and a second wave would cause a displacement of 2cm at the same point, the total displacement of the medium at that point will be 7 cm. If the two waves you have drawn are traveling together in the same medium, what would be the maximum displacement of the medium at any point? ______
4. Using the third colored pencil and on the same graph grid, draw the wave that represents the overall displacement of the medium when the two original waves are traveling in the same medium at the same time. Record your color choice in the legend. What is the amplitude of this resultant wave? ______How far would the resultant wave travel in one period of the resultant wave? ______
5. On the second blank grid on the worksheet, draw the original two waves as they would appear a time equal to one-quarter of a period after the first graph. Use the same color for each wave as you used previously. Remember that wave 1 is moving to the right and wave 2 is moving to the left. On the same grid, use the third colored pencil to draw the resultant wave for this situation. What is the amplitude of the resultant wave in this case? ______
6. Repeat Step 5, this time showing the original two waves at a time equal to one-half a period later than in the first graph. What is the amplitude of the resultant wave in this case? ______
7. Repeat Step 5 one more time, this time showing the original two waves at a time equal to three-quarters of a period later than in the first graph. What is the amplitude of the resultant wave in this case? ______
8. Which of the situations would you categorize as having a “constructive” effect taking place? ______Why do you think this is so? ______
9. Which of the situations would you categorize as having a “destructive” effect taking place? ______Why do you think this is so?
10. Look at the resultant waves on the series of graphs. Are there any locations where the medium carrying the wave would have a vertical displacement of zero at all times? ______Locations where there is no vertical motion of the medium carrying a wave are called nodes. In terms of wavelengths, how far apart are the nodes of the resultant wave located? ______
11. Again observe the resultant waves on your graphs. Are there any locations where the medium carrying the wave would oscillate in a vertical direction between maximum positive displacement and maximum negative displacement? ______Locations where the medium carrying a wave oscillates between maximum positive and negative displacement are called antinodes. In terms of wavelengths, how far apart are the antinodes of the resultant wave located? ______
12. In terms of wavelengths, what is the distance between a node and an antinode on the resultant wave ? ______
13. If a wave is oscillating relatively quickly, the position of the wave at all times will appear to be superimposed. Show this on the second wave worksheet drawing all four resultant waves superimposed on each other. How does this compare with the standing wave shown in your text?
14. List the following information for your standing wave:
amplitude______
wavelength ______
distance between nodes and antinodes (in terms of wavelengths)______
15. Does the appearance of the standing wave change over time? If so how? If not, why not? Explain.______
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Wave Worksheet
y (cm) / 2t = 0 s / 1
0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / x (cm)
-1
-2
y (cm) / 2
t = (1/4)T s / 1
0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / x (cm)
-1
-2
y (cm) / 2
t = (1/2)T s / 1
0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / x (cm)
-1
-2
y (cm) / 2
t = (3/4)T s / 1
0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / x (cm)
-1
-2
Wave Worksheet (Standing Wave)
y (cm) / 2all resultant waves / 1
0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18 / x (cm)
-1
-2
Legend: Wave 1 moving right
Wave 2 moving left
Superposition of both waves
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Standing Waves – Part 2 – Standing Waves on A String
Objective: Determine the frequencies to make standing waves of different wavelengths
Equipment:
Wave resonator, Clamp,support rod, pulley, two types of string, electronic balance, meter stick, 500 gram hooked mass 2 jumper cables, function generator.
An example of the apparatus will be set up for you as shown below:
The following information is given for this experiment:
L (length between resonator and pulley) = 2.0m. If you are cutting the string, cut about 2.5 m to obtain L = 2.0 m
(m/L)1 (thicker white string) = 7.00 x 10-4 kg/m
(m/L)2 (thinner white/green string) = 3.15 x 10-4 kg/m
1. Determine the tension on the string (assume the tension is due only to the 500 g mass):
T______N
2. Calculate the speed of the wave along the String 1 (thicker white string) and String 2 (thinner white/green). Show your work below:
v1 = ______m/s v2 = ______m/s
3. Look at the illustration on page 1. Note that it shows 2 segments making up the length, L, of the string between resonator and pulley. How many wavelengths are shown in this illustration? ______
4. Draw a picture below of a standing wave that has only one segment making up L.
How many wavelengths are shown in your illustration? ______
5. Based on your answers above, calculate the frequency necessary to generate a standing wave of one segment on the thicker white string. Show your work, below and record value under expected frequency in Data Table 1 below
6. Now do the experiment to check your prediction! Dial in the frequency that generates a standing wave for your string. Fill in the appropriate values and calculate the % difference between experimental value and expected value for frequency.
7. Repeat the procedure for standing waves of 2 and 3 segments.
8. Repeat the procedure for the second, thinner string. Remember to use v2 in your calculations for expected frequency
DATA TABLE FOR STRING #1 (THICKER)
Number of segments / Wavelength, l in terms of L (L/2, L etc) / Expected Frequency (Hz) / Experimental Frequency (Hz) / % Difference1
2
3
DATA TABLE FOR STRING #2 (THINNER)
Number of segments / Wavelength, l in terms of L (L/2, L etc) / Expected Frequency (Hz) / Experimental Frequency (Hz) / % Difference1
2
3
9. Were the frequencies for the lighter string different that those for the heavier string? If so, why do you think that was so? ______
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