Two closed organ pipes when sounded simultaneously give 4 beats/second. If longer pipe has a length of 1m, then length of shorter pipe will be (v=300 m/s)

Options

(a) 185.5 cm
(b) 94.9 cm
(c) 90 cm
(d) 80 cm

Correct Answer:

94.9 cm

Explanation:

n₂ – n₁ = 4, For closed pipe, n = V/4l
(V/4l₂) – (V/4l₁) = 4 ⇒ (V/4l₂) – (V/4×1) = 4
(300/4l₂) – (300/4) = 4 ⇒ 75/l₂ = 4 + 75 ⇒ 75/l₂ = 79
⇒ l₂ = (75/79) met = (75×100)/79 = 94.9 cm.