Question

If two air columns of lengths $100cm$ and $101cm$ sounding in their fundamental note gave $17$ beats in $20$ seconds, then the velocity of sound will be

• A. $277.8m/s$
• B. $300m/s$
• C. $250m/s$
• D. $343.4m/s$

Answer 1

Answer: (D)

$343.4m/s$

Given, $l_1=100cm=1m$
$l_2=101cm=1.01cm$
Number of beats per second,
$n=17/20$
Let the velocity of sound is $v$ and $v_1,v_2$ be the fundamental frequencies of vibrations of two air columns.
Then, $v_1=\frac{v}{4l_1}=\frac{v}{4\times 1}=\frac{v}{4}$
and $v_2=\frac{v}{4\times 1.01}=\frac{v}{4.04}$
As, $v_1-v_2=n$
$\Rightarrow \frac{v}{4}-\frac{v}{4.04}=\frac{17}{20}$
$\Rightarrow v=343.4m/s$.