Homework Solution - Standing Waves and Pressure in a Closed Tube

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In summary, the problem involves a vertical tube that is closed at one end and open to air at the other. The air pressure is known, and mercury is poured into the tube to shorten the effective length for standing waves. The question asks for the absolute pressure at the bottom of the mercury column when the fundamental frequency of the shortened air-filled tube is equal to the third harmonic of the original tube. The pressure at the bottom of the mercury is unrelated to the wave between the top of the mercury and the open end, so the density of mercury can be used to solve for the pressure. This pressure is calculated to be 1.68 x 10^5 Pa.
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3ephemeralwnd
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Homework Statement



A vertical tube is closed at one end and open to air at the other end. The air pressure is 1.01 x 10^5 Pa. The tube has a length of 0.75 m. Mercury (mass density = 13,600 kg/m3) is poured into it to shorten the effective length for standing waves. What is the absolute pressure at the bottom of the mercury column, when the fundamental frequency of the shortened air-filled tube is equal to the third harmonic of the original tube?
ANS: 1.68 x 10^5 Pa

Homework Equations


Ive been given the equations Fn = nv/4L for tubes with one open end, although I can't seem to find any way to relate pressure and waves, can anyone help?
 
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hi 3ephemeralwnd! :smile:

(try using the X2 icon just above the Reply box :wink:)
3ephemeralwnd said:
Ive been given the equations Fn = nv/4L for tubes with one open end, although I can't seem to find any way to relate pressure and waves, can anyone help?

the pressure at the bottom of the mercury has nothing to do with the wave between the top of the mercury and the open end …

it's just a cute way of asking two totally unrelated :rolleyes: questions at once! :biggrin:

(so just use the density of mercury :wink:)
 

FAQ: Homework Solution - Standing Waves and Pressure in a Closed Tube

1. What are waves?

Waves are a type of disturbance that travels through a medium or empty space. They can be categorized as either mechanical waves, which require a medium to travel through, or electromagnetic waves, which can travel through empty space.

2. How are waves measured?

Waves can be measured in terms of their frequency, wavelength, and amplitude. Frequency is the number of waves that pass a given point in a certain amount of time. Wavelength is the distance between two consecutive points on a wave with the same phase. Amplitude is the maximum displacement of particles in a wave from their resting position.

3. What is the relationship between frequency and wavelength?

The relationship between frequency and wavelength is inverse; as the frequency of a wave increases, its wavelength decreases, and vice versa. This is known as the wave equation: v = fλ, where v is the wave velocity, f is the frequency, and λ is the wavelength.

4. What are the different types of waves?

There are several different types of waves, including transverse waves, longitudinal waves, and surface waves. Transverse waves have particles that vibrate perpendicular to the direction of the wave's propagation, while longitudinal waves have particles that vibrate parallel to the direction of the wave. Surface waves are a combination of both transverse and longitudinal waves, and they travel along the surface of a medium.

5. How are waves used in everyday life?

Waves have many practical applications in everyday life. Some examples include using radio waves for communication, using microwaves for cooking, and using sound waves for music and communication. Waves are also used in medical imaging techniques like X-rays and ultrasound. Additionally, waves play a crucial role in weather and oceanic phenomena such as wind and ocean waves.

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