Question

The fundamental frequency of an open organ pipe is equal the third harmonic of closed organ pipe. if the length of closed organ pipe is 20cm,tge length of open organ pipe is ? answer with solution

Answer 1

Hello Dear.

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.


Hope it helps.

Answer 2

Let length of open organ pipe is L
And v is speed of sound wave .
fundamental frequency of open organ pipe is given by η₁ = v/2L
Frequency of 3rd harmonic of closed organ pipe is given by η₂ = 3v/4L'
[For (2n-1)th harmonic in case of closed organ pipe is given by (2n-1)/4L]
Here L' is the length of closed organ pipe .

A/C to question,
fundamental frequency resonate with frequency of 3rd harmonic of closed organ pipe .
η₁ = η₂
v/2L = 3v/4L'
⇒ 4L' = 6L
⇒2L' = 3L
L' = 20 cm is given
∴ L = 2/3 × 20 = 40/3 cm

Hence, length of open organ pipe = 13.33 cm