PURPOSE: In this laboratory the frequency that produce standing waves are calculated and compared to the expected value. These standing waves for a given tension is equivalent to allowed resonant frequency for a stirring with the given tension and length.
THEORY: Traveling waves can be produced by two waves of equal frequencies and amplitudes traveling in opposite directions. For standing waves to exist on a string of a given length the length of the string must be an integer multiple of one half the wavelength of the wave. The velocity of a wave on a string is given by
Where F is the tension in the string and m is the linear mass density (m = M/L). The velocity of a wave is also given by
where f is the frequency and l is the wavelength. By adjusting the tension in the string different numbers of segments can be produced in the standing wave.
EQUIPMENT: Computer and VideoPoint software.
PROCEDURE:
1. Work with the pasco152, pasco 153, and pasco154.
2. Click on points on the string where no vibration occurs. The step-by-step procedure is listed below.
3. Calibrate the video.
4. Record the linear mass density of the string and it s frequency.
5. Determine the length of one vibrating segment by taking the difference in the position of the end of one vibrating segment. Determine the Wavelength of the wave by doubling this length.
6. Calculate the wave velocities and tension in the string by using the equations from the theory.
Start VideoPoint.
Click left mouse button while the pointer is anywhere inside the "about VideoPoint" dialogue box.
In the "open" dialogue box do the following.
Select the drive letter of the CD drive in which VideoPoint is located.
Select movies folder and the appropriate folder under movies (here the "pasco" folder).
Under filename select the appropriate file to be loaded (Paxco152, Pasco153, and Pasco154).
Press "OK".
The "Number of points" dialogue box will appear. Make sure "1" is selected and press "OK". The movie and software should now be loaded.
On the menu bar select "Movie" and "Full Screen" using the left mouse button.
Record data -When the cursor is inside the movie screen it appears as a target. Place this target cursor on the left end of the vibrating string and press the left mouse button. Place the cursor on the right end of the string and press the left mouse button again. You need only two data points to get the length of the vibrating string
Calibrate the movie.
Move the cursor to the "meter stick" tool button at the left of the screen (6th button from top) and click the left mouse button.
The "Scale Movie" dialogue box appears. Change the known length to 0.80 it you select to mark the 10 cm and the 90 cm positions of the meter stick since all the stick is not visible. Select continue with the left mouse button.
Put the target cursor on the left end of the meter stick(10 cm) in the first movie frame and press left mouse button - repeat for the right end of the meter stick (90 cm).
On the menu bar select "Movie" and "Normal Size".
Transfer the data
With cursor inside table area click left mouse button to select table.
Put mouse in title area of table and click and hold left mouse button
and drag the
table to top of window.
Place the pointer on lower right corner of table (cursor should be double arrow) and drag the corner of the table to make the table larger so all the data can be seem.
Record the X-position of each end of the vibrating string in the data in data table.
QUESTIONS:
1. Every thing else being constant, what must the tension in the string do in order to double the number of segments produced on the string?
2. Is much error is being introduced into the calculation of the velocity by the linear mass density changing because the string is stretching?
3. Are the waves on the string longitudinal waves or transverse waves.
4. What are the units for the slope of the wavelength verses wave velocity graph?
Linear mass density m = M/L = __________
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