Question

Consecutive resonances occur at wavelengths of 8 m and 4.8 m in an organ pipe closed at one end. What is the length of the organ pipe? (Note: Resonances occur at L = nλ/ 4, where L is the pipe length, λ is the wavelength, and n = 1, 3, 5,…)

Answer 1

Length of pipe 6 meters

Step-by-step explanation:

Answer 2

Length of the organ pipe is 6 meters.

Step-by-step explanation:

Let resonance occur at wavelengths of 8 m at n and wavelength of 4.8 m at (n+2). We know that resonance occurs at,

`L=n(\lambda)/(4)`

`L=n(8)/(4)`

L = 2 n.................(1)

And,

`L=(n+2)(4.8)/(4)`

`L=n(8)/(4)`

`2n=1.2n+2.4` (from equation (1))

n = 3

Put the value of n in equation (1). So,

`L=2* 3=6\ m`

So, the length of the organ pipe is 6 meters. Hence, this is the required solution.