Optimizing Resonance Length for Closed-End Pipe with a Tuning Fork

In summary, the question asks for the shortest length of a closed tube that will resonate with a tuning fork of frequency 512 Hz as a piston is slowly withdrawn. Using the equation L=1/4λ and f=v/(4L), the answer is found to be 0.16m, assuming a speed of sound of 340m/s.
  • #1
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Homework Statement


A tube is closed at one end by a piston which is slowly withdrawn as a tuning fork of frequency 512 Hz is sounded over it. What is the shortest length of pipe which will resonate with the fork?
(Speed of sound is 340m/s)


Homework Equations


L=1/4λ
f=v/(4L)

The Attempt at a Solution


Since the question wants the shortest length for resonance, so set L=1/4λ → 4L=λ
Then, f=v/(4L) → 512=340/(4L) → L=0.16m

Is the answer and the way i approached this question correct?
 
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  • #2
Exhausted said:
)

The Attempt at a Solution


Since the question wants the shortest length for resonance, so set L=1/4λ → 4L=λ
Then, f=v/(4L) → 512=340/(4L) → L=0.16m

Is the answer and the way i approached this question correct?

It is correct but a little rounding error.

ehild
 
  • #3
Thanks :D
 

1. What is a closed end pipe?

A closed end pipe is a type of resonator that is open on one end and closed on the other. It can be made of any material, such as metal, wood, or plastic, and is commonly used in musical instruments like flutes and organ pipes.

2. How do sound waves travel through a closed end pipe?

Sound waves travel through a closed end pipe by creating an alternating pattern of high and low pressure zones. When the sound wave reaches the closed end, it reflects back and creates a standing wave inside the pipe. This standing wave has nodes at the closed end and antinodes at the open end, which determines the pitch of the sound produced.

3. What is the difference between an open and closed end pipe in terms of sound production?

The main difference between an open and closed end pipe is the standing wave pattern that is created inside the pipe. In a closed end pipe, there is a node at the closed end and an antinode at the open end, while in an open end pipe, there is an antinode at both ends. This results in different frequencies and pitches of sound being produced.

4. How does the length of a closed end pipe affect the pitch of the sound produced?

The length of a closed end pipe directly affects the pitch of the sound produced. As the length of the pipe increases, the wavelength of the sound decreases, resulting in a higher frequency and higher pitch. Conversely, as the length decreases, the frequency and pitch also decrease.

5. Can a closed end pipe produce multiple pitches or notes?

Yes, a closed end pipe can produce multiple pitches or notes. This is because the standing wave inside the pipe can have multiple nodes and antinodes, which correspond to different frequencies and pitches. By changing the length or shape of the pipe, different pitches can be produced.

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