1. Resonant frequencies of a string fixed at both ends

For a string fixed at both ends, allowed resonant frequencies are:

where:

• $n = 1,2,3,\dots$
• $f_1$ is the fundamental (lowest resonant frequency).

So all resonant frequencies are equally spaced by $f_1$.

2. Use the given frequencies

Two resonant frequencies are given:

And it is stated that there are no other resonant frequencies between them.

This means these two frequencies must be consecutive harmonics.

Hence their difference equals the fundamental frequency:

3. Check

If $f_1 = 105\,\text{Hz}$, then:

So these are indeed consecutive harmonics ($3^{\text{rd}}$ and $4^{\text{th}}$), with no resonance in between.

4. Final answer

The lowest resonant frequency is:

So the correct option is A.

5. Comparison with stored answer

Stored correct answer: A

My derived answer: A

They agree.