Two adjacent natural frequencies of an organ pipe are determined to be 986 Hz and 1102 Hz. (Assume the speed of sound is 343 m/s.) (a) Calculate the fundamental frequency of this pipe. (b) Calculate the length of this pipe.

Respuesta :

Answer:

The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.

Explanation:

Given that,

First frequency = 986 Hz

Second frequency = 1102 Hz

We need to calculate the length of the pipe

Using formula of length

[tex]\Delta f=f_{2}-f_{1}=\dfrac{nv}{2L}[/tex]

Put the value into the formula

[tex]1102-986=\dfrac{1\times343}{2\times L}[/tex]

[tex]L=\dfrac{343}{2\times116}[/tex]

[tex]L=1.48\ m[/tex]

We need to calculate the fundamental frequency of this pipe

[tex]f_{1}=\dfrac{nv}{2L}[/tex]

Put the value into the formula

[tex]f_{1}=\dfrac{1\times343}{2\times1.48}[/tex]

[tex]f_{1}=115.8\ Hz[/tex]

Hence, The fundamental frequency and the length of the pipe are 115.8 Hz and 1.48 m.

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