Suppose you have a tube of length L containing a gas whose temperature you want to take, but you cannot get inside the tube. One end is closed, and the other end is open but a small speaker producing

Question

Suppose you have a tube of length L containing a gas whose temperature you want to take, but you cannot get inside the tube. One end is closed, and the other end is open but a small speaker producing sound of variable frequency is at that end. You gradually increase the frequency of the speaker until the sound from the tube first becomes very loud. With further increase of the frequency, the loudness decreases but then gets very loud again at still higher frequencies. Call $f_{0}$ the lowest frequency at which the sound is very loud. ( $M$ is the molar mass of the gas, $Y$ is the ratio of its heat capacities, and $R$ is the ideal gas constant.)

Options:(select one or more)

Answer:

A, C

Solution:

$f_{0} = \frac{v}{4 L}$

$v = \frac{γ RT}{M}$

Substitute $v = 4 L f_{0}$ :

$4 L f_{0} = \frac{γ RT}{M}$

$16 L^{2} f_{0}^{2} = \frac{γ RT}{M}$

Solving for $T$ : $T = \frac{16 M L ^{2} f _{0}^{2}}{γ R}$

$f_{3} = 3 f_{0}$

TestHub · Accepted Answer

f 0 ​ = 4 L v ​ v = M γ RT ​ ​ Substitute v = 4 L f 0 ​ : 4 L f 0 ​ = M γ RT ​ ​ 16 L 2 f 0 2 ​ = M γ RT ​ Solving for T : T = γ R 16 M L 2 f 0 2 ​ ​ f 3 ​ = 3 f 0 ​

Physics - Sound Wave Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion

JEE Advanced (2028)