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
[tex]f=\dfrac{v}{2L}\\\Rightarrow L=\dfrac{v}{2f}[/tex]
It can be seen that
[tex]L\propto \dfrac{1}{f}[/tex]
So,
[tex]\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[/tex]
The ratio of the piccolo's length to the flute's length is 0.49806
