Question

A piccolo and a flute can be approximated as cylindrical tubes with both ends open. The lowest fundamental frequency produced by one kind of piccolo is 516.1 Hz, and that produced by one kind of flute is 257.0 Hz. What is the ratio of the piccolo's length to the flute's length?

Answer 1

Answer:

0.49806

Explanation:

v = Velocity of wave

L = Length of tube

p denotes piccolo

f denotes flute

The fundamental frequency with both ends open is given by

$f=\dfrac{v}{2L}\\\Rightarrow L=\dfrac{v}{2f}$

It can be seen that

$L\propto \dfrac{1}{f}$

So,

$\dfrac{L_p}{L_f}=\dfrac{f_f}{f_p}\\\Rightarrow \dfrac{L_p}{L_f}=\dfrac{257}{516} \\\Rightarrow \dfrac{L_p}{L_f}=0.49806$

The ratio of the piccolo's length to the flute's length is 0.49806