Model No. WA-9857
Experiment 2: Teachers’ Notes–Standing Waves In Strings
23
®
Be sure to measure from the sudden force change, not the relatively slow variation that may occur
before the actual pluck. It may be helpful to repeat the measurement a few times and take the
average value.
∆
t = 3.4 × 10
-2
s
v = L/
∆
t = 68.8 m/s
Conclusions
1) In the sample data above, all three calculations of v were within 5% of each other. (The first
two calculations were exactly equal, but that is not typical.) With a sample rate of 1000 Hz,
the uncertainty of the pulse timing measurement was about 1 ms, or 3% of
∆
t, which would
account for much of the 5% deviation observed.
2) The method based on frequency and wavelength was probably the most accurate because it
involved only one measurement, length, which was probably accurate to within a few
millimeters (or about 0.1%). The frequency of the AC power is usually very close to its
nominal value, so you can ignore its uncertainty. You can also use the voltage sensor plugged
into the output of the power supply to measure the frequency. Do not attempt to measure the
voltage directly from the wall.
Experiment 2:
Teachers’ Notes–Standing Waves In Strings
The density of the recommended string is about 0.266 g/m, so it’s best to use a balance readable to
0.01 g. If you have a less-precise balance, have a long piece of string available for students to
measure the length and mass of.
Standing waves of n = 1, 2 and 3 are fairly easy to achieve. Standing waves of n
≥ 4
may require
mass adjustments of 1 g or less. You can make these adjustments by adding pieces of paper to the
hanging mass. It will suffice to estimate the mass to within 0.5 g.
Analysis Method 1
L = 0.987 m
f = 60.0 Hz
µ
= 2.66 × 10
-4
kg/m
Number of
Segments
Hanging
Mass (g)
Uncertainty
(g)
v
F
µ
(m/s)
v
λ
f
(m/s)
% Deviation
1
380
10
120
118
1.7%
2
95
2
60.
59.2
1.3%
3
41
1
39
39.5
1.3%
4
22.5
1
29
29.6
2.0%
5
14
1
23
23.7
3.0%
6
9
1
20
19.7
1.5%
Содержание WA-9857
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