An organ pipe A, with both ends open, has fundamental frequency 300 Hz. The third harmonic of another organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. The lengths of pipe A and B are (speed of sound in air = 343 m/s)

Question

An organ pipe A, with both ends open, has fundamental frequency 300 Hz. The third harmonic of another organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. The lengths of pipe A and B are (speed of sound in air = 343 m/s) (A) 57.2 cm and 42.9 cm (B) 57. 2 cm and 45.8 cm (C) 42.9 cm and 32.2 cm (D) 42.9 cm and 34.0 cm

Tardigrade Admin · Accepted Answer

Given that fundamental frequency of open organ pipe

(A) = 300 Hz

f_{1} = 300 Hz = \frac{v}{2 l _{1}} \dots

(i)
Frequency of second harmonic-of open organ pipe

(A) = \frac{v}{l _{1}}

and frequency of third harmonic of closed organ pipe

= \frac{3 v}{4 l _{2}}

Now according to question

\frac{v}{l _{1}} = \frac{3 v}{4 l _{2}}

\Rightarrow \frac{l _{1}}{l _{2}} = (\frac{4}{3}) \dots

(ii)
Form Eq. (i), we get

300 = \frac{343}{2 l _{1}}

l_{1} = \frac{343}{600} = 52.16 = 57.2 c m

Now from Eq. (ii), we get

l_{2} = \frac{3}{4} \times l_{1}

= \frac{3}{4} \times 57.2 = 42.9 c m

Q. An organ pipe A, with both ends open, has fundamental frequency 300Hz. The third harmonic of another organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. The lengths of pipe A and B are (speed of sound in air = 343m/s)

57.2 cm and 42.9 cm

57. 2 cm and 45.8 cm

42.9 cm and 32.2 cm

42.9 cm and 34.0 cm

Q. An organ pipe $A$ , with both ends open, has fundamental frequency $300 Hz$ . The third harmonic of another organ pipe $B$ , with one end open, has the same frequency as the second harmonic of pipe $A$ . The lengths of pipe $A$ and $B$ are (speed of sound in air = $343 m / s)$