Two adjacent natural frequencies of an organ pipe are AMT determined to be 550 Hz and 650 Hz. Calculate (a) the M fundamental frequency and (b) the length of this pipe.

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Two adjacent natural frequencies of an organ pipe are AMT determined to be 550 Hz and 650 Hz. Calculate (a) the M fundamental frequency and (b) the length of this pipe.

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CarliReifsteck CarliReifsteck · Answer 1 · 2025-03-23T03:52:49-04:00

Answer:

The fundamental frequency and length of the pipe are 100 Hz and 1.7 m.

Explanation:

Given that,

Frequency f = 550 Hz

Frequency f' = 650 Hz

We know that,

AMT pipe is open pipe.

(b). We need to calculate the length of the pipe

Using formula of organ pipe

[tex]f=\dfrac{nv}{2L}[/tex]

For 550 Hz,

[tex]550=\dfrac{n\times340}{2L}[/tex]...(I)

For 650 Hz,

[tex]650=\dfrac{(n+1)\times340}{2L}[/tex]...(II)

From equation (I) and (II)

[tex]550-650=\dfrac{340}{2L}-\dfrac{340}{L}[/tex]

[tex]L=\dfrac{340}{2\times100}[/tex]

[tex]L=1.7\ m[/tex]

(a). We need to calculate the fundamental frequency for n = 1

Using formula of fundamental frequency

[tex]=f=\dfrac{n\lambda}{2L}[/tex]

put the value of L

[tex]f=\dfrac{1\times340}{2\times1.7}[/tex]

[tex]f=100\ Hz[/tex]

Hence, The fundamental frequency and length of the pipe are 100 Hz and 1.7 m.