Question

A whistle whose air column is open at both ends has a fundamental frequency of $5100 \,Hz$. If the speed of sound in air is $340\, ms^{-1}$, the length of the whistle, in cm, is

• A. 44684
• B. 44837
• C. $5$
• D. 20-Mar

Answer 1

Answer: (B)

44837

Answer 2

$f=\frac{c}{2\ell} \Rightarrow \ell=\frac{v}{2f}=\frac{340}{2\times5100}=\frac{1}{30}m=\frac{10}{3}cm$For an open pipe, the frequency
$f=\frac{v}{2 l}$
$\Rightarrow 5100=\frac{340}{2 \times l}$
$l=\frac{340}{5100 \times 2}$
$\Rightarrow l=\frac{2}{30 \times 2}=\frac{1}{30} m$
$l=\frac{100}{30}=\frac{10}{3} \,cm$