Fundamental Frequency of a String

[NeRdHeRd]

Homework Statement

A string with a length of 2.5m has two adjacent resonances at frequencies 112 Hz and 140 Hz. Determine the fundamental frequency of the string?

A. 14 Hz
B. 28 Hz
C. 42 Hz
D. 56 Hz
E. 70 Hz


2. The attempt at a solution

Since I am not sure how to begin solving this I divided the two Resonances by each of the given solutions to the problem and based on that I came up with 28 Hz as being correct.

112/28 = 4 and 140/28 = 5 since these are adjacent and the others were not I chose 28 Hz

I'm sure there is some type of formula or a method of solving this. If anyone can help me with solving this the correct way it would be appreciated. Thank you.

 

[learningphysics]

I think the method you solved it is right. One shortcut you can take is 140Hz-112Hz = 28Hz.

So the answer must be 28Hz. (reason being (n+1)*F - n*F = 1*F = F... so if 140 and 112 are adjacent frequencies, F must be 28).

But you should also make sure that 140/28 gives an integer and 112/28 gives an integer... which they both do...