Wavelengths of standing waves on a string

[googlyeyes]

Homework Statement

Consider a string of length L held fixed at both ends. The string can be shaken up and down and, at certain frequencies, the result will be a standing wave pattern on the string. Find the five longest wavelengths (call them λ1, λ2, λ3, λ4, and λ5) of the standing wave patterns that fit on the string. Write your answers in terms of L.

Homework Equations

c=fλ

The Attempt at a Solution

λ1 = L
λ2 = L/2
λ3 = L/4
λ4 = L/8
λ5 = L/16

 

[BOYLANATOR]

Have you tried drawing the possible waves?

 

[googlyeyes]

Yes but I am not sure my thinking is right. I am thinking that in order for the wavelength to fit on the string it must either be L (the length of the string) or half, half again, etc. for the entire wave to fit (i am new to physics). Is this thinking completely wrong?

 

[BOYLANATOR]

The best way to understand is to see it...

 

[googlyeyes]

So to find the five longest wavelengths do i need to use the formula i gave or should it be obvious (in terms of L) from drawing it?

 

[BOYLANATOR]

You don't need to use your formula. If the distance between the two black blocks in my image is L. Can you state what the wavelengths of each of the three waves are in terms of L?

 

[googlyeyes]

Ok so the 1st one would be 2L, the 2nd would be L and the 3rd would be 2/3L?

 

[BOYLANATOR]

Ok so the 1st one would be 2L, the 2nd would be L and the 3rd would be 2/3L?

Correct. What about the 4th and 5th?

 

[googlyeyes]

Um 4th would be 1/2L, 5th would be 2/5L?

 

[BOYLANATOR]

Yup!

 

[googlyeyes]

Thank you so much! I understand this concept so much better now! I really appreciate your help!