Understanding Standing Wave Loops: Solving a 60 Hz Frequency Question

[yesgirl10]

Hi everyone,
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!

 

[jedishrfu]

Your way gave a v of 30m/s but the books way gives it correctly as 180m/s so I'd say use the books way. If they were equivalent then you'd have the same v for both.

 

[dauto]

Your method is correct. The book's method is messed up.

 

[AlephZero]

I agree with dauto. In the first line of the book solution, the wavelength is not 3m. The question says the rope is 3m long.

 

[yesgirl10]

Okay, thanks everyone for the feedback! Really appreciate it. :)

 

[Redbelly98]

The phrase "waves in a rope 3 m long" could have been intended to mean that the waves are 3 m long -- which is bad English and would mean the error is in the writing of the question.

Either way, the book is messed up.

 

[jedishrfu]

The phrase "waves in a rope 3 m long" could have been intended to mean that the waves are 3 m long -- which is bad English and would mean the error is in the writing of the question.

Either way, the book is messed up.

Yeah, that's how I interpretted it when I saw how the book did it and was wondering if there was a lost comma after rope.

Sometimes this happens when they decide to change a problem to make it more difficult by changing the wording without or values and forgetting to change the answer sheet too.

I once took a latin course where the first edition of the review book had sentences in latin to convert to english and the second version had the same sentences in english and asked you to convert them to latin. I lucked out when I recognized that fact and got a perfect score which made the teacher suspicious until I explained what I discovered and she had to acquiese to the situation.