For a certain organ pipe, three successive resonance frequencies are observed at 425 Hz , 595 Hz and 765 Hz respectively. If the speed of sound in air is 340 m / s, then the length (in m) of the pipe is?

Question

For a certain organ pipe, three successive resonance frequencies are observed at 425 Hz , 595 Hz and 765 Hz respectively. If the speed of sound in air is 340 m / s, then the length (in m) of the pipe is? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The ratio of frequencies is 425: 595: 765=5: 7: 9 So clearly as consecutive frequencies are odd multiples of a fundamental frequency v and pipe is a closed pipe closed at both ends. Hence, (5 v/4 L)=425 ⇒ (5(340)/4 L) =425 L =(5 × 340/4 × 425)=1 m

Q. For a certain organ pipe, three successive resonance frequencies are observed at 425Hz,595Hz and 765Hz respectively. If the speed of sound in air is 340m/s, then the length (in m) of the pipe is?

The ratio of frequencies is 425:595:765=5:7:9 So clearly as consecutive frequencies are odd multiples of a fundamental frequency v and pipe is a closed pipe closed at both ends. Hence, 4L5v​=425 ⇒4L5(340)​=425 L=4×4255×340​=1m

Q. For a certain organ pipe, three successive resonance frequencies are observed at $425 Hz, 595 Hz$ and $765 Hz$ respectively. If the speed of sound in air is $340 m / s$ , then the length (in $m$ ) of the pipe is?