- Computers are needed for lab this week
- One electronic balance is needed for lab this week
- Use wave theory and the physical characteristics of the vibrating string to measure the wave speed
- Before each lab, I check the following settings on the function generator:
- Power on, press 100 and sine wave buttons
- Frequency ~10 Hz
- Amplitude knob at the 3 o'clock position
- Power off
- L is the length of the string (from end of vibrating finger to pulley), and set to just under 2-meters (about 196±1 cm). You get higher amplitudes from shorter string lengths!
- I think that many measure L wrong because they read the measuring tape incorrectly!
- Adjusting the frequency on the function generator requires a very light touch to keep from overshooting the resonant frequency. Some students will have a lot of trouble with this, so you'll need to watch them carefully until they get the hang of it. Make sure they get the first couple of frequencies correct!
- Since the data table contains λ, many students want to use it in their Excel graph, but don't know how to insert/format Greek letters. A learning opportunity!
- My data; note that the frequency starts with 550-g of tension starts around 30 Hz and increments by around 15 Hz, and with 1050-g of tension starts around 40 Hz and increments by around 20 Hz:
-
| n |
λ (m) |
1/λ (1/m) |
f (550g) (Hz) |
f (1050g) (Hz) |
| 2 |
1.831 |
0.546 |
29.8 |
40.2 |
| 3 |
1.221 |
0.819 |
48.7 |
65.4 |
| 4 |
0.916 |
1.092 |
62.6 |
87.7 |
| 5 |
0.732 |
1.365 |
79.6 |
108.3 |
| 6 |
0.610 |
1.638 |
93.5 |
129.6 |
| 7 |
0.523 |
1.912 |
109.7 |
150.1 |
| 8 |
0.458 |
2.185 |
125.2 |
168.0 |
- From the graph of this data, I get
- v {550 g} = 57.4 m/s
- v {1050 g} = 77.8 m/s
- At right is my graph (click for a larger view):
- A sample string is provided (hanging on the blackboard or coat rack) so that students can calculate the linear density, μ using the sample string mass (m = 3.9 g) and sample string length ( lstring= 2.317 m), which gives μ = 1.68×10-3 kg/m
- With this data, I get the following results:
- v {550 g} = 56.6 m/s (1% diff); fundamental frequency, f = 15.5 Hz
- v {1050 g} = 78.3 m/s (0.5% diff); fundamental frequency, f = 21.4 Hz
- There does not seem to be any correlation between the two methods in which one velocity is always higher than the other
-
- Common mistakes:
- Students will use L (the length of the string they used on the apparatus) with the sample string length! There's a note in the instructions and the board, but it's still a problem. *sigh*
- Weak students will want to compare the wave speed between the two tensions. *double-sigh*
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