Question

Two organ pipes of lengths 40 cm and 40.4 cm oscillate together. The pair produces sound of variable intensity and between two consecutive maximas, we get 0.25 s. Then the speed of sound in air is about

• A. 330 m/s
• B. 342 m/s
• C. 324 m/s
• D. 360 m/s

Answer 1

The correct option is C 324 m/s

$f=\frac{v}{2l}$

$f_1=\frac{v}{2\left(0.4\right)}$

$f_2=\frac{v}{2\left(0.404\right)}$

Beat frequency

$f_1-f_2=\frac{v}{0.8}-\frac{v}{0.808}$

$=4$

$v\left\{\frac{0.008}{0.8\times 0.808}\right\}=4$

$v=\frac{4\times 0.8\times 0.808}{0.008}$

$=4\times 80.8$

$\approx$ $4\times 81=324m/s$