PASCO WA-9611_13 SONOMETER - Manual (Page 19)

15
012-03489E Sonometer
Analysis
➀ Use your measured string length, the fundamental frequency, and the equation V = λν
to determine the velocity
of the wave on the string for each value of tension and linear density that you used.
➁ Determine the functional relationship between the speed of the wave (V) and the wire tension (T). This can be
accomplished using either of the following three methods. If you are not familiar with these procedures, you
might want to try all three.
➤ NOTE: Options A and B are easily performed using a computer with graphical analysis
software.
A. Plot a graph of V versus T, with V on the y-axis. If the graph is not a straight line, try plotting V versus some
power of T (such as T
2
, T
1/2
, etc.), until you get a straight line.
B. Assume that the functional relationship is of the form V = kT p . Then ln V = p ln T + ln k, where p and k are
unknown constants. Then, if lnV is plotted against the independent variable lnT, a straight line will be ob-
tained having a slope p, where p is lnV/ lnT and ln k is the y-intercept.
C. Many calculators have the ability to do power regressions or linear regressions on the logarithms of V and T.
This will accomplish essentially what the graph of method B did.
➂ Using one of the methods above, determine the functional relationship of the speed of the wave (V) to the linear
density of the string (
µ
).
Conclusions
Characterize the resonant modes of a vibrating wire. That is:
➀ Determine a mathematical relationship that describes the wavelengths of the waves that form standing wave
patterns in a wire of length L (see Experiment 1).
➁ Use your answer to question 1, and the expression V = λν
, to determine the resonant frequencies of a wire of
length L.
➂ Use your experimental results to write an expression for the resonant frequencies of a vibrating wire in terms of
T,
µ
, and L.