How Long is an Organ Pipe That Resonates at 128Hz?

In summary, open end resonant length is a measurement used to determine the fundamental frequency of a resonant system by calculating the distance between the open end of a resonator and the nearest node of a standing wave. This is done by knowing the speed of sound, frequency of the standing wave, and number of antinodes. The open end resonant length is significant in understanding the properties and behavior of the system and can be changed by adjusting the physical dimensions or properties of the medium. It affects sound waves by determining the strongest vibration frequency and the harmonic frequencies that can be produced by the resonator.
  • #1
soulja101
61
0

Homework Statement


an organ pipe, open at both ends, esonantes ats its 1st resonant lenth with a frequency of 128hz. what is thelength of the pipe if the speed of sound is 346m/s


Homework Equations


the open colum patterns


The Attempt at a Solution


i just can't get it
 
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  • #2
From the univeral wave equation, what is the wavelength at the given frequency and wave speed?

From the open column patterns, how many wavelengths does the length of an open pipe contain? (Hint, the answer is not 1)
 
  • #3
to work

As a scientist, it is important to carefully consider the given information and use relevant equations to solve the problem. In this case, the problem is asking for the length of an open organ pipe that resonates at its 1st resonant length with a frequency of 128Hz, given the speed of sound is 346m/s.

To solve this problem, we can use the equation for the resonant frequency of an open organ pipe: f = nv/2L, where f is the frequency, n is the harmonic number (in this case, 1st harmonic), v is the speed of sound, and L is the length of the pipe.

Substituting the given values into the equation, we get:

128Hz = (1)(346m/s)/(2L)

Solving for L, we get:

L = (346m/s)/(2*128Hz) = 1.352m

Therefore, the length of the pipe is 1.352m. It is important to carefully consider the units and use appropriate conversions when solving problems in science.
 

Related to How Long is an Organ Pipe That Resonates at 128Hz?

1. What is open end resonant length?

Open end resonant length is a measurement of the distance between the open end of a resonator and the nearest node of a standing wave. It is used to determine the fundamental frequency of a resonant system.

2. How is open end resonant length calculated?

To calculate open end resonant length, the speed of sound in the medium, the frequency of the standing wave, and the number of antinodes in the standing wave must be known. The formula for calculating open end resonant length is: L = (n + 0.5) * (wavelength / 2), where n is the number of antinodes and the wavelength is equal to the speed of sound divided by the frequency.

3. What is the significance of open end resonant length?

The open end resonant length is significant because it determines the fundamental frequency of a resonant system. This frequency is important in understanding the behavior and properties of the system, and can also be used in various applications such as musical instruments, acoustic design, and measurement techniques.

4. How does open end resonant length affect sound waves?

The open end resonant length affects sound waves by determining the frequency at which a resonator will vibrate most strongly. This frequency, also known as the fundamental frequency, is the lowest frequency at which a standing wave can exist in the resonator. It also determines the harmonic frequencies that can be produced by the resonator.

5. Can open end resonant length be changed?

Yes, open end resonant length can be changed by adjusting the physical dimensions of the resonator. For example, changing the length of an open-ended tube will change its open end resonant length and therefore its fundamental frequency. Additionally, the open end resonant length can also be affected by the properties of the medium in which the sound waves are traveling, such as temperature and pressure.

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