Determining Harmonic Frequency of 1m Pipe

In summary: Expert summarizerIn summary, the conversation was about determining the frequency of the first harmonic in a pipe open at both ends, with a length of 1 m, and a velocity of sound in air of 343 m/s. The formula used to calculate frequency is f = v/2L, and the correct answer is 171.5 Hz. The forum user had a small mistake in their calculation, but the expert clarified it for them and encouraged them to keep trying.
  • #1
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Homework Statement



A pipe has a length of 1 m.
Determine the frequency of the first harmonic if the pipe is open at each end. The
velocity of sound in air is 343 m/s.
Answer in units of Hz

Homework Equations



f = v/2L

The Attempt at a Solution



I just did another problem like this and got it right but for some reason I keep getting this wrong. I plugged in f = (343)/2(1) = 171.5. But this is wrong. Not sure what I'm supposed to do.
 
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  • #2




Thank you for your question. From your attempt at a solution, it seems like you are on the right track. However, there might be a mistake in your calculation. The formula for calculating frequency for the first harmonic in a pipe open at both ends is f = v/2L, where v is the velocity of sound and L is the length of the pipe. In your calculation, you have correctly plugged in the values for v and L, but you have forgotten to divide by 2. The correct answer should be f = (343 m/s)/2(1 m) = 171.5 Hz. I hope this helps clarify the confusion. Please let me know if you have any further questions. Keep up the good work!


 

FAQ: Determining Harmonic Frequency of 1m Pipe

1. What is the purpose of determining the harmonic frequency of a 1m pipe?

The purpose of determining the harmonic frequency of a 1m pipe is to understand the natural resonant frequency of the pipe, which is the frequency at which the pipe will naturally vibrate and produce the loudest sound. This information is important for musicians, engineers, and scientists studying sound waves and acoustics.

2. How is the harmonic frequency of a 1m pipe calculated?

The harmonic frequency of a 1m pipe can be calculated using the formula v/2L, where v represents the speed of sound and L represents the length of the pipe. This formula applies to open-ended pipes, such as a flute or organ pipe, which produce the fundamental frequency and all of its harmonics. For closed-ended pipes, like a clarinet or oboe, the formula is 3v/4L.

3. What factors can affect the harmonic frequency of a 1m pipe?

The harmonic frequency of a 1m pipe can be affected by several factors, including the material of the pipe, temperature, and the speed of sound in the surrounding medium. Additionally, the length and diameter of the pipe can also impact the harmonic frequency, as well as any obstructions or changes in the shape of the pipe.

4. How is the harmonic frequency of a 1m pipe measured?

The harmonic frequency of a 1m pipe can be measured using a variety of techniques, such as using an oscilloscope to visualize the vibrations of the pipe or using a frequency analyzer to determine the exact frequency being produced. Another method is to use a tuning fork and adjust the length of the pipe until the sound from the pipe matches the frequency of the tuning fork.

5. Why is it important to accurately determine the harmonic frequency of a 1m pipe?

Accurately determining the harmonic frequency of a 1m pipe is important for several reasons. It can help musicians tune their instruments, engineers design efficient acoustic systems, and scientists study the properties of sound waves. In addition, understanding the harmonic frequency of a 1m pipe can also aid in the diagnosis and treatment of certain medical conditions, such as vocal cord disorders.

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