The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m / s, then the length of closed organ pipe is

Question

The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m / s, then the length of closed organ pipe is (A) 41 cm (B) 37 cm (C) 31 cm (D) 80 cm

Tardigrade Admin · Accepted Answer

For an open pipe, fundamental frequency

v = \frac{v}{2 L}

∴ L = \frac{v}{2 v} = \frac{330}{2 \times 300} = \frac{11}{20}

As frequency of

1^{st}

overtone of open pipe

=

frequency of

1^{st}

overtone of closed pipe

∴ \frac{2 v}{2 L} = \frac{3 v}{4 L ^{'}}

or

L^{'} = \frac{3 L}{4} = \frac{3}{4} \times \frac{11}{20} = 0.4125 m = 41.25 c m \approx 41 c m

Q. The fundamental frequency of an open organ pipe is 300Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330m/s, then the length of closed organ pipe is

41 cm

37 cm

31 cm

80 cm

For an open pipe, fundamental frequency v=2Lv​ ∴L=2vv​=2×300330​=2011​ As frequency of 1st overtone of open pipe = frequency of 1st overtone of closed pipe ∴2L2v​=4L′3v​ or L′=43L​=43​×2011​=0.4125m=41.25cm≈41cm

Q. The fundamental frequency of an open organ pipe is $300 Hz$ . The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $330 m / s$ , then the length of closed organ pipe is