Standing Waves Under Boundary Conditions

In summary, the problem involves a thin pipe placed vertically in a cylindrical bucket filled with water. The pipe is at resonance with a tuning fork held over it. The goal is to find the volume of water in the bucket at this moment. One should look into standing sound waves in tubes and attempt to solve the problem using this concept.
  • #1
sugz
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Homework Statement


See the figure below. A thin pipe, open
arrow-10x10.png
at both ends, with length 0.400 m and 1.0 cm diameter is placed vertically in a cylindrical bucket so that it nearly touches the flat bottom of the bucket, which has an area of 0.100 m2 . The air temperature is 22o C. Water is slowly poured into the bucket until a sounding tuning fork of frequency 440 Hz, held over the pipe, produces resonance. Find the volume of the water in the bucket at this moment. (Assume the same water level in the pipe and in the bucket, as shown in the diagram.)
upload_2015-2-27_10-42-5.png


Homework Equations

The Attempt at a Solution


How would you suggest I go about it?
 
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  • #2
sugz said:

The Attempt at a Solution


How would you suggest I go about it?

Look after standing sound waves in tubes, and show your attempt to solve the problem.

 

1. What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in stationary points of maximum and minimum amplitude, known as nodes and antinodes, respectively.

2. What are boundary conditions in relation to standing waves?

Boundary conditions refer to the constraints placed on a standing wave by the medium it is traveling through. These conditions can include fixed endpoints, changes in medium density, or changes in medium length.

3. How are standing waves formed under boundary conditions?

Standing waves are formed when a wave with a certain frequency and amplitude travels through a medium and reflects off of a boundary. The reflected wave combines with the original wave, creating interference patterns that result in stationary points.

4. What are some real-life examples of standing waves under boundary conditions?

Standing waves can be observed in musical instruments, such as the strings of a guitar or the air columns in wind instruments. They can also be seen in electromagnetic waves, such as radio waves bouncing between buildings in a city.

5. How do boundary conditions affect the properties of standing waves?

Boundary conditions play a crucial role in determining the frequency, wavelength, and amplitude of a standing wave. Changes in boundary conditions can alter the pattern of nodes and antinodes, as well as the overall energy and propagation of the wave.

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