A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm , both vibrating in fundamental mode. The velocity of sound is ______ m s - 1 .

Step-by-step solution

The formula to calculate the fundamental frequency in a closed pipe is given by f c = v 4 l 1 . . . 1 And, that in an open pipe is given by f o = v 2 l 2 . . . 2 Given that f c - f o = 7 . . . 3 From equations (1), (2) and (3), it follows that v 4 × 150 - v 2 × 350 = 7 ⇒ v 600 cm - v 700 cm = 7 ⇒ v 6 m - v 7 m = 7 ⇒ v 1 42 = 7 ⇒ v = 42 × 7 = 294 m s - 1