Question

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. if the lenght pf the closed organ pipe is 20cm the lenght of open pipe is

Answer 1

Given, Here in Question ⇒

Fundamental Frequency for the Open orange pipe is given by ⇒ ν/2l'

Where,
ν (neu) = Frequency &
 l' is the length of the open orange pipe.

Also, We know,
Third Harmonic of the orange pipe = 3ν/4l
where,
ν = frequency & 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.


Thus, the length of the open orange pipe = 13.33 cm.


Hope it helps.

Answer 2

Answer:

Fundamental Frequency for the Open orange pipe is given by ⇒ ν/2l'

Where,

ν (neu) = Frequency &

 l' is the length of the open orange pipe.

Also, We know,

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

where,

ν = frequency & 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.