Fundamental frequency 2

Question

A string, stretched between two fixed posts, forms standing wave resonances at 330 Hz and 385 Hz.

What is the greatest possible value of its fundamental frequency?

Answer 1

For a string, the wavelengths are

1/2 L, L, 3/2 L, 2 L, 5/2 L, and so on.

The corresponding frequencies increase by factors of

2, 3, 4, 5, ...

and so on.

Your two frequencies are 330 Hz and 385 Hz, which differ by 55 Hz.

We don't know what multiples of the fundamental these are, so...

( n + d ) F - ( n ) F = 55 / d

( n + d ) F = 385

( n ) F = 330

The smallest integer solution is n = 6 and d = 1.

That would make the fundamental F = 55 Hz.