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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,…)

Respuesta :

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,

[tex]L=n\dfrac{\lambda}{4}[/tex]

[tex]L=n\dfrac{8}{4}[/tex]

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

And,

[tex]L=(n+2)\dfrac{4.8}{4}[/tex]

[tex]L=n\dfrac{8}{4}[/tex]

[tex]2n=1.2n+2.4[/tex] (from equation (1))

n = 3

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

[tex]L=2\times 3=6\ m[/tex]

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

acruz2007

Answer:

Length of pipe 6 meters

Explanation:

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