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

Answer:

Length of the organ pipe is 6 meters.

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,

$L=n\dfrac{\lambda}{4}$

$L=n\dfrac{8}{4}$

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

And,

$L=(n+2)\dfrac{4.8}{4}$

$L=n\dfrac{8}{4}$

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

n = 3

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

$L=2\times 3=6\ m$

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

Answer 2

Answer:

Length of pipe 6 meters

Explanation: