The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the

Question

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm , the length of the open organ pipe is:

Accepted Answer

1. The fundamental frequency of an open organ pipe (

f_{o p e n}

) is:

f_{o p e n} = \frac{v}{2 l _{o p e n}}

2. The third harmonic of a closed organ pipe (

f_{c l ose d, 3}

) is:

f_{c l ose d, 3} = \frac{3 v}{4 l _{c l ose d}}

3. Given

f_{o p e n} = f_{c l ose d, 3}

:

\frac{v}{2 l _{o p e n}} = \frac{3 v}{4 l _{c l ose d}}

\frac{1}{l _{o p e n}} = \frac{3}{2 l _{c l ose d}}

l_{o p e n} = \frac{2 l _{c l ose d}}{3}

Given

l_{c l ose d} = 20 cm

:

l_{o p e n} = \frac{2 \times 20}{3} = \frac{40}{3} \approx 13.33 cm

The closest option provided is

13.2 cm

.

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 cm$ , the length of the open organ pipe is:

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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20cm, the length of the open organ pipe is: