PHYS 210L Final 1st Exercise with Solution, Fall 2008
American University of Beirut · Introductory Physics Laboratory II · 3 pages · with solution
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Physics 210L Exam + Solution (first question only)
I.
Standing Waves on a Stretched String:
We perform a standing waves on a stretched string experiment by varying the length
of the string and fixing the mode to 2; so that every time we vary the length, the
frequency varies in such a way that only 2 harmonics are observed.
The hanging mass was measured to be 1Kg using an analog scale of smallest division
of 0.1g.
The following data were recorded:
L (m)
f (Hz)
0.5
182.4
0.6
151.3
0.7
128.8
0.8
113.2
0.9
99.1
a.
Write the necessary equations to find an appropriate relation between f and L.
(Specify your xi and yi).
b. Find the slope. What does it represent?
After inserting (x,y) to the calculator in linear regression mode, we get:
Slope = B = 93.066
Intercept = A = -3.89
c.
Find the error on the slope.
Δ = 5 (11.6284) – (7.46)2
= 2.4904
Slope = 93 ± 1
d. Find linear density μ along with the error on it.
xi = 1/L
yi = f (Hz)
2
182.4
1.67
151.3
1.43
128.8
1.25
113.2
1.11
99.1
xi = 1/L
yi = f (Hz)
ynew = 93.066 xi - 3.89
ei = ynew - yi
(ei)2
2
182.4
183.43
1.03
1.0609
1.67
151.3
151.53
0.23
0.0529
1.43
128.8
129.19
0.39
0.1521
1.25
113.2
112.44
-0.76
0.5776
1.11
99.1
99.41
0.31
0.0961
sum = 7.46
1.9396
μ = (1.13 ± 0.03)×10-3 Kg/m = (1.13 ± 0.03) g/m
e.
Compare your results to the literature value of 1.12 g/m
1.12 lies in the interval [1.13 – 2(0.03), 1.13 + 2(0.03)] = [1.07, 1.19] therefore
our results are accurate.