Question

show that the fundamental frequency of an open organ pipe is double than the frequency of closed organ pipe .

Answer 1

Given :- 

Fundamental Frequency for the Open orange pipe = ν/2l'

where, ν = Frequency and l' is the length of the open orange pipe.

Third Harmonic of the orange pipe = 3ν/4l

where, ν = frequency

and l is the length of the Closed orange pipe = 20 cm.

Now, According to the Question,

3ν/4l = ν/2l'

⇒ 3/(4 × 20) = 1/2l'

⇒ 3/80 = 1/2l'

⇒ 2l' = 80/3

⇒ l' = 40/3

⇒ l' = 13.33 cm.

Hence, the length of the open orange pipe is 13.33 cm.

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Answer 2

Answer:

The fundamental frequency of an open organ pipe is double than the frequency of closed organ pipe.

Proof:

Fundamental frequency of an open organ pipe:

ν1 = v/2L1

Or, v = 2L1ν1     - (i)

Fundamental frequency of an closed organ pipe:

ν2 = v/4L2

Or, v = 4L2ν2   - (ii)

From (i) & (ii),

2L1ν1 = 4L2ν2

Or, 2ν1 = 4ν2        {As it is given that L1=L2}

Or, ν1 = 2ν2

Hence proved.

Hope this helps!