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In a pipe open at both ends the fundamen...

In a pipe open at both ends the fundamental note is produced-when its length is equal to

A

`lamda`, (wavelength of sound)

B

`lamda/4` ( quarter wavelength)

C

`lamda/2`(half wavelength)

D

`2lamda` (twice wavelength)

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The correct Answer is:
To determine the length of a pipe open at both ends that produces the fundamental note, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Concept of Open Pipes**: - In a pipe that is open at both ends, the ends of the pipe are points of maximum amplitude, known as anti-nodes. The points in between where the amplitude is zero are called nodes. 2. **Identify the Fundamental Frequency**: - The fundamental frequency (or first harmonic) is the lowest frequency at which the pipe can resonate. For an open pipe, this corresponds to the simplest standing wave pattern. 3. **Visualize the Standing Wave**: - For the fundamental mode in an open pipe, the standing wave pattern consists of one full wave fitting into the length of the pipe. This means that there are two anti-nodes at the ends and one node in the middle. 4. **Relate Length to Wavelength**: - The relationship between the length of the pipe (L) and the wavelength (λ) for the fundamental frequency in an open pipe can be expressed as: \[ L = \frac{\lambda}{2} \] - This indicates that the length of the pipe is equal to half the wavelength of the sound wave. 5. **Conclusion**: - Therefore, the length of the pipe open at both ends that produces the fundamental note is equal to half of the wavelength of the sound wave produced. ### Final Answer: The length of the pipe open at both ends that produces the fundamental note is equal to \( \frac{\lambda}{2} \).
To determine the length of a pipe open at both ends that produces the fundamental note, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Concept of Open Pipes**: - In a pipe that is open at both ends, the ends of the pipe are points of maximum amplitude, known as anti-nodes. The points in between where the amplitude is zero are called nodes. 2. **Identify the Fundamental Frequency**: ...
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