Question

The fundamental frequency of open organ pipe is 250hz . Third harmonics of closed organ pipe is equal to second harmonics of open organ pipe. Find length of closed organ pipe ..vel of air 343m/s

Answer 1

Given:

Fundamental frequency of open organ pipe is 250Hz. Third harmonics of closed organ pipe is equal to second harmonics of open organ pipe.

Velocity of air = 343 m/s

To find:

Length of closed organ pipe

Calculation:

For open organ pipe , the fundamental frequency is 250 Hz , let length be l

$\therefore \: \dfrac{v}{2l} = 250$

$= > 2l = \dfrac{v}{250}$

$= > 2l = \dfrac{343}{250}$

$= > l = \dfrac{343}{500} \: cm \: \: \: \: \: \: ....(1)$

Now , 3rd harmonic of closed organ pipe is equal to 2nd harmonic of open organ pipe :

Let length of closed organ pipe be l2

$\therefore \: \dfrac{3v}{4(l2)} = \dfrac{v}{l}$

$= > \: \dfrac{3}{4(l2)} = \dfrac{1}{l}$

$= > l2 = \dfrac{3l}{4}$

$= > l2 = \dfrac{3}{4} \times \dfrac{343}{500}$

$= > l2 = 0.5145 \: m$

$= > l2 = 51.45 \: cm$

So length of closed organ pipe is 51.45 cm

Answer 2

${ \underline{ \underline{ \tt{ \huge{ \green{question}}}}}}$

The fundamental frequency of open organ pipe is 250 Hz . Third harmonic of closed organ pipe is equal to second harmonics of open organ pipe. Find length of closed harmonic pipe.

velocity of air = 343 m/s

${ \underline{ \underline{ \huge{ \tt{ \green{solution}}}}}}$

let the fundamental frequency of open organ pipe be f•.

and in the question f• = 250 Hz

second harmonics of open organ pipe = 2f•

= 2 × 250 Hz = 500 Hz

According to the question

Third harmonic of closed organ pipe = second harmonic of closed organ pipe

then , third harmonic of closed organ pipe = 500 Hz

third harmonic of closed organ pipe = 3v/ 4l

where, l is the length of closed organ pipe

& v is the velocity of air

${ \dagger{ \purple{ \tt{ \: \: \: \: 500 \: hz \: = \: \frac{3v}{4l}}}} }$

${ \rightarrow{ \tt{ \purple{ \: 4l \: = \: \frac{3v}{500} }}}}$

${ \rightarrow{ \purple{ \tt{ \: l \: = \: \frac{3 \times 343}{500 \times 4}}}}}$

${ \boxed{ \boxed{ \green{ \tt{ \: l \: = \: 0.5145 \: m \: = \: 51.45 \: cm}}}}}$

the length of closed organ pipe is 51.45 cm