Question

A string under tension 1080N, of mass per unit length 0.003kg/m has many resonant frequency on such frequency is 450 Hz and the next higher frequency is 600Hz How long is the string?

Answer 1

Answer on Question #72282-Physics-Mechanics-Relativity

A string under tension 1080N, of mass per unit length $0.003\mathrm{kg / m}$ has many resonant frequency on such frequency is $450\mathrm{Hz}$ and the next higher frequency is $600\mathrm{Hz}$ . How long is the string?

Solution

$$f = \frac {n}{2 l} \sqrt {\frac {T}{\mu}}$$ $$f ^ {\prime} = \frac {n ^ {\prime}}{2 l} \sqrt {\frac {T}{\mu}}$$ $$f ^ {\prime} - f = \frac {n ^ {\prime} - n}{2 l} \sqrt {\frac {T}{\mu}}$$ $$f ^ {\prime} - f = \frac {1}{2 l} \sqrt {\frac {T}{\mu}}$$

The length is

$$l = \frac {1}{2 (f ^ {\prime} - f)} \sqrt {\frac {T}{\mu}} = \frac {1}{2 (6 0 0 - 4 5 0)} \sqrt {\frac {1 0 8 0}{0 . 0 0 3}} = 2 m.$$

Answer: $2m$