Tuning fork standing wave in a water pipe

In summary, the question is asking for the wavelength of the sound emitted by a tuning fork, with the distance between two positions of maximum loudness being x. The correct answer is D, where the wavelength is equal to 2x. This can be determined using the equations for pipes with two ends open and one end open and one end closed. The pipe will resonate at the harmonics of the tuning fork frequency and the difference between the first and second harmonic is half a wavelength. Therefore, x represents half of the wavelength and the wavelength itself is equal to 2x.
  • #1
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Homework Statement


IMG_1132.jpg

The question is as follows:
The distance between the two positions of maximum loudness is x
What is the wavelength of the sound emitted by the tuning fork ?
A. x/2
B. x
C. 3x/2
D. 2x

the correct answer is answer D.

Homework Equations


Pipe with two ends open
λn= 2L /n

Pipe with one end open and one end closed
λn= 4L/n

The Attempt at a Solution



At the positions of maximum loudness, there must be an antinode, but the water acts like a closed pipe so there should be a node at the surface of the water. If there is an antinode at the positions of maximum loudness the fundamental frequency would have a wavelength in distance x of λ/2. but that doesn't make sense since there should be a node so now I am confused and also don't understand how to know how many loops there should be.
 

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  • #2
The pipe will resonate at the harmonics of the tuning fork frequency. See picture below. When the pipe length is increased by x, what fraction of the wavelength is added to it?
Pipes.png
 

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  • #3
kuruman said:
The pipe will resonate at the harmonics of the tuning fork frequency. See picture below. When the pipe length is increased by x, what fraction of the wavelength is added to it?
View attachment 222898

I understand now, when the water surface was at the dotted line, there was still a little bit of space above in the pipe, the sound produced was the first harmonic, then when the water moved down another loud sound was heard: The second harmonic and the difference between the first and second harmonic is half a wavelength.
Therefore x=λ/2
and λ= 2x

Thanks
 

1. What is a tuning fork standing wave in a water pipe?

A tuning fork standing wave in a water pipe is a phenomenon that occurs when a tuning fork is placed at the open end of a pipe filled with water. The vibrations of the tuning fork create pressure waves in the water, which reflect off the closed end of the pipe and create a standing wave pattern.

2. How does a tuning fork standing wave in a water pipe work?

The tuning fork creates vibrations that travel through the water and create areas of high and low pressure. These pressure waves reflect off the closed end of the pipe and interfere with each other, creating a standing wave pattern with nodes (points of no movement) and antinodes (points of maximum movement).

3. What factors affect the standing wave pattern in a tuning fork water pipe experiment?

The length of the pipe, the frequency of the tuning fork, and the speed of sound in water all affect the standing wave pattern. The length of the pipe determines the wavelength of the wave, the frequency of the tuning fork determines the number of nodes and antinodes, and the speed of sound in water determines the distance between adjacent nodes and antinodes.

4. What is the significance of the standing wave pattern in a tuning fork water pipe experiment?

The standing wave pattern in a tuning fork water pipe experiment demonstrates the principles of resonance and standing waves. It also allows for the calculation of the speed of sound in water and the frequency of the tuning fork using the known length of the pipe.

5. How is a tuning fork standing wave in a water pipe used in real-world applications?

Tuning fork standing waves in water pipes are used for various acoustic experiments and demonstrations, such as determining the speed of sound in different mediums. They are also used in musical instruments, such as the pipe organ, to produce specific frequencies and create beautiful sounds. Additionally, similar principles are applied in medical ultrasound technology to create and detect standing waves in the body for imaging purposes.

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