Question

In a closed organ pipe, the first resonance occurs at 25 cm, at what length of pipe, the second resonance will occur?
(1) = 75 cm
(2) > 75 cm
(3) < 75 cm
(4) <or= 75 cm
Kindly explain.​

Answer 1

Answer:

option (1) = 75 cm

Explanation:

Data provided in the question:

The first resonance occurs at length = 25 cm

Now,

The length of point of resonance in a closed organ pipe is given as:

L =  $\frac{n\lambda}{4}$

here,

n = 1, 3 , 5 .........

thus,

for first resonance n = 1

or

25 cm =  $\frac{1\times\lambda}{4}$

or

$\frac{\lambda}{4}$ = 25 cm

and,

the second resonance will occur at n = 3

thus,

L = $\frac{3\lambda}{4}$ cm

thus,

on substituting the value, we get

L = 3 × 25 cm

or

L = 75 cm

Hence,

The correct answer is option (1) = 75 cm