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Chapter 10: Problem 1465

Tube \(A\) has both ends open while tube \(B\) has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube \(\mathrm{A}\) and \(\mathrm{B}\) is \(\ldots \ldots \ldots\) (A) \(1: 2\) (B) \(1: 4\) (C) \(2: 1\) (D) \(4: 1\)

Short Answer

Expert verified
The ratio of the fundamental frequency of Tube A and Tube B is 2:1.

Step by step solution

01

Formula for fundamental frequency of a tube

: For a tube with both ends open or both ends closed: \(f_{1}=\dfrac{v}{2L}\) For a tube with one end open, and one end closed: \(f_{2}=\dfrac{v}{4L}\) where \(f_{1}\) is the fundamental frequency of an open-closed tube, \(f_{2}\) is the fundamental frequency of an open-open tube, \(L\) is the length of the tube, and \(v\) is the speed of sound in air.
02

Evaluate the fundamental frequency of Tube A (both ends open)

: Using the formula for tubes with both ends open: \(f_{1}=\dfrac{v}{2L}\)
03

Evaluate the fundamental frequency of Tube B (one end closed)

: Using the formula for tubes with one end open: \(f_{2}=\dfrac{v}{4L}\)
04

Find the ratio of fundamental frequencies

: Now we will find the ratio of the fundamental frequencies of Tube A and Tube B: \(\dfrac{f_{1}}{f_{2}}=\dfrac{\dfrac{v}{2L}}{\dfrac{v}{4L}}\) The 'v' and 'L' get canceled out, leaving: \(\dfrac{f_{1}}{f_{2}}=\dfrac{2}{1}\) Thus, the ratio of fundamental frequency of Tube A to Tube B is 2:1, which corresponds to option (C). Answer: \(\boxed{\text{(C)}\ 2:1}\).

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Most popular questions from this chapter

A person standing in a stationary lift measures the periodic time of a simple pendulum inside the lift to be equal to \(\mathrm{T}\). Now, if the lift moves along the vertically upward direction with an acceleration of $(\mathrm{g} / 3)$, then the periodic time of the lift will now be \((\mathrm{A}) \sqrt{3} \mathrm{~T}\) (B) \(\sqrt{(3 / 2) \mathrm{T}}\) (C) \((\mathrm{T} / 3)\) (D) \((\mathrm{T} / \sqrt{3})\)

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