A source of frequency of 60 Hz is used to make waves in a rope that is 3.0m long. It takes 0.10s for the waves to travel from one fixed end of the rope to the other. How many loops are in the standing wave in the rope?

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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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A source of frequency of 60 Hz is used to make waves in a rope that is 3.0m long. It takes 0.10s for the waves to travel from one fixed end of the rope to the other. How many loops are in the standing wave in the rope? 

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I don't understand what Dstands for or why it equals λ/2. Does it always equal λ/2 or is that just specific to this question. Is there another way to solve this problem? Thanks.

d=3.0m

t=0.10s

v=?

 

v=d/t

=3.0m/0.10s

=30m/s

 

v=30m/s

f=60 Hz

λ=?

 

λ=v/f

=30m/s/60 Hz

=0.5m

 

DN= λ/2

=0.5m/2

=0.25m

 

# of loops= d/DN

= 3.0m/0.25m

= 12 loops

 

 

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