Question

Two closed organ pipes, when sounded simultaneously gave 4 beats per sec. If longer pipe has a length of 1m. Then length of shorter pipe will be,

(v = 300 m/s)

• A. 185.5 cm
• B. 94.9 cm
• C. 90 cm
• D. 80 cm

Answer 1

Answer: (B)

94.9 cm

Answer 2

For first pipe $n_{1} = \frac{v}{4l_{1}}$and for second pipe $n_{2} = \frac{v}{4l_{2}}$

So, number of beats = $n_{2} - n_{1} = 4$

$\Rightarrow 4 = \frac{v}{4}\left( \frac{1}{l_{2}} - \frac{1}{l_{1}} \right) \Rightarrow 16 = 300\left( \frac{1}{l_{2}} - \frac{1}{1} \right)$ $\Rightarrow$ $l_{2} = 94.9cm$