# Standing wave question

I just have a question about the correct procedure to follow to complete a question.

The question is: A source of frequency of 60 Hz is used to make waves in a rope 3.0m long. It takes 0.10 s 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?

I got the same answer as the textbook, however, the procedure to get my answer was different.

The textbook did: v=fλ=(60Hz)x(3.0m)=180m/s

v=Δd/Δt or Δd=v(Δt)=180m/s(0.10s)=18m

Since each wavelength is 3.0m long, the number of wavelengths is 18m/3m=6

Because there are two loops for every wavelength, the are 12 loops.

The way I did it: v=Δd/Δt=(3m)/(0.10s)=30m/s

λ=v/f=(30m/s)/(60Hz)=0.5m

Because the string is 3m long, 0.5mx __ =3.0m

3.0m/0.5m=6 Thus, there are 6 wavelengths in the 3.0m of string but because 1 wavelength = 2 loops, there are 12 loops.

So, I have two questions

**1) Is the way I solved this question accurate and reliable? Or did I just get lucky that this method happened to work with these numbers.**

**2) The question states that the string is 3.0m long. Then the textbook stated it as the wavelength (v=fλ=(60Hz)x(3.0m)=180m/s). Can someone please help me understand why this is okay? I thought it was the length of the string or distance from the start to the end. **

Thank you!

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

**3. The attempt at a solution**

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