In a large laboratory, two waves with the same amplitude and wavelength travel i
ID: 1423861 • Letter: I
Question
In a large laboratory, two waves with the same amplitude and wavelength travel in opposite directions along the same rope. The two waves interfere, and the result is a standing wave on the rope given as
y(x,t) = 0.300 sin(2.50x) cos(6.35t)
where the numerical values have the appropriate SI units.
a) What is the separation between a node and an antinode?
b) If there are seven nodes, including a node on one end, and if there is an antinode on the other end, find the length of the rope. (The antinode could be generated by attaching one end of the rope to a motor.)
Explanation / Answer
a) Separation between a node and an antinode =lambda/4 =1/4*pi/2k =pi/2k=0.6283 m
b) L=6*lambda/2 + lambda/4 =6*pi/k + pi/2k = 6*3.14/2.5 +3.14/2*2.5 = 6*1.257 +0.6283
L=8.17 m
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