Consider a pipe 12 cm in length. Find by how much percentage does the ...
Exactly half wavelength fits the pipe,
When one end is closed then
of a wavelength fits the pipe
= 50%
The correct answer is: 50
View all questions of this test
Consider a pipe 12 cm in length. Find by how much percentage does the ...
Introduction:
In physics, when a pipe is closed at one end, it undergoes a change in its fundamental frequency. The fundamental frequency is the lowest frequency at which a system vibrates. In the case of a pipe, it refers to the lowest resonant frequency at which the air column inside the pipe vibrates.
Given Information:
- Length of the pipe (original) = 12 cm
- Pipe is originally open at both ends
- Pipe is closed from one side
Analysis:
When a pipe is open at both ends, it supports a standing wave pattern with an antinode at each end and a node in the middle. This pattern allows for the oscillation of the air column at the fundamental frequency.
When the pipe is closed from one side, the closed end acts as a node, and the open end continues to act as an antinode. This change in boundary conditions alters the standing wave pattern inside the pipe, resulting in a change in the fundamental frequency.
Calculating the Change in Fundamental Frequency:
To find the change in the fundamental frequency, we need to compare the original frequency with the new frequency after closing one end of the pipe.
Formula:
The fundamental frequency of a pipe open at both ends is given by the equation:
f = v/2L
Where:
- f is the frequency
- v is the speed of sound in air
- L is the length of the pipe
Calculations:
Let's assume the speed of sound in air, v, remains constant.
Original frequency, f1 = v/2L (where L = 12 cm)
New frequency, f2 = v/4L (where L = 12 cm minus the length of the closed end)
Calculating the difference in the two frequencies:
Δf = f2 - f1 = v/4L - v/2L = -v/4L
To express the change in frequency as a percentage, we need to find the ratio of the change to the original frequency:
Percentage change = (Δf/f1) * 100
Substituting the values:
Percentage change = (-v/4L) / (v/2L) * 100 = -1/2 * 100 = -50%
Conclusion:
The change in the fundamental frequency when a pipe originally open at both ends is closed from one side is a decrease of 50%.