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An air-filled pipe is found to have successive harmonics at 435 Hz , 725 Hz , and 1015 Hz . It is unknown whether harmonics below 435 Hz and above 1015 Hz exist in the pipe. What is the length of the pipe?

Respuesta :

Answer:

L = 1.706 m

Explanation:

Three successive harmonics in the pipe is given as

[tex]f_1 = 435 Hz[/tex]

[tex]f_2 = 725 Hz[/tex]

[tex]f_3 = 1015 Hz[/tex]

now if we take the ratio of all frequency

then we have

f1 : f2 : f3 = 435 : 725 : 1015 = 3 : 5 : 7

since the ratio of consecutive frequency is in ratio of odd numbers so this must be 3rd harmonics, 5th harmonics and 7 harmonics

And as per the formula we have

[tex]f_1 = \frac{3v}{4L}[/tex]

[tex]435 = \frac{3(340)}{4L}[/tex]

[tex]L = 1.706 m[/tex]

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