A pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s. What is the length of this

Question

A pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s. What is the length of this pipe? Answer in units of cm.

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Mackenzie 7 months 2021-10-08T17:36:01+00:00 1 Answer 0 views 0

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    2021-10-08T17:37:22+00:00

    Answer:

    51.72 cm.

    Step-by-step explanation:

    We have been given that a pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s. We are asked to find the length of the pipe.

    First of all, we will find the wavelength using following formula.

    [tex]\text{Wave speed}=\text{Frequency}\times \text{Wave length}[/tex]

    [tex]331\frac{\text{m}}{\text{s}}=320\text{ Hz}\times \text{Wave length}[/tex]

    We know that Hz is equal to [tex]\frac{1}{s}[/tex].

    [tex]331\frac{\text{m}}{\text{s}}=320\frac{1}{\text{s}}\times \text{Wave length}[/tex]

    [tex]331\text{ m}=320\times \text{Wave length}[/tex]

    [tex]\text{Wave length}=\frac{331}{320}\text{ m}[/tex]

    [tex]\text{Wave length}=1.034375\text{ m}[/tex]

    Length of the pipe would be half of the wave-length.

    [tex]\text{Length of pipe}=\frac{1.034375}{2}\text{ m}=0.5171875\text{ m}[/tex]

    Since the length of pipe is in meters, so we will convert it into cm.

    1 m = 100 cm

    [tex]\text{0.5171875 m}=0.5171875\times 100\text{ cm}=51.71875\text{ cm}\approx 51.72\text{ cm}[/tex]

    Therefore, the length of the pipe would be 51.72 cm.

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