April 2022 – JEE First

A collection of problems on standing waves

April 24th, 2022jeefirst0 Comments

Question 1

A string of length $L$ is clamped at each end and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves cannot be:

$L/2$
$L$
$2L/3$
$2L$
$4L$

Question 2

If the speed of sound is 340 m/s, the length of the shortest open-closed pipe that resonates at 218 Hz is:

23 cm
17 cm
39 cm
78 cm
1.6 cm

Question 3

At $20^\circ {\rm C}$ , a pipe open at both ends resonates at a frequency of 440 Hz. At what frequency does the same pipe resonate on a particularly cold day when the speed of sound is 3 percent lower than …

Heat transferred along two paths

April 10th, 2022jeefirst0 Comments

JEE Advanced 2014 Paper 1, Question 20

A thermodynamic system is taken from an initial state $i$ with internal energy $U_{i} = 100 \, {\rm J}$ to the final state $f$ along two different paths $i a f$ and $i b f$ , as schematically shown in the figure. The work done by the system along the paths $a f, i b$ and $b f$ are $W_{a f} = 200 \, {\rm J}, W_{i b} = 50 \, {\rm J}$ and $W_{b f} = 100 \, {\rm J}$ respectively. The heat supplied to the system along the path $i a f, i b$ and $b f$ are $Q_{i a f}, Q_{i b}$ and $Q_{b f}$ respectively. If the internal energy of the system in the state $b$ is $U_{b} = 200 \, {\rm J}$ and $Q_{i a f} = 500 \, {\rm J}$ , the ratio $Q_{b f}/Q_{i b}$ is

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Solution

The problem gives us partial information about internal energies, heat transferred, and work done at various points in the PV diagram. We …

A collection of Doppler effect problems

April 9th, 2022jeefirst0 Comments

Here is a set of four problems on the Doppler shift of sound waves. The solutions to the problems are given at the end. If you need a refresher on the Doppler effect, the following note might be useful: How does Doppler effect work?

Question 1

While standing at a crosswalk, you hear a frequency of 560 Hz from an approaching police car. After the police car passes and is moving away from you, you hear a frequency of 480 Hz. What is the speed of the police car (take speed of sound to be $v=343$ m/s)?

13.1 m/s
21.1 m/s

…

An adiabatic bubble

April 1st, 2022jeefirst0 Comments

IIT-JEE 2008 Paper 1, Question 38,39,40

A small spherical monoatomic ideal gas bubble $\left(\gamma=\frac{5}{3}\right)$ is trapped inside a liquid of density $\rho_{\ell}$ (see figure below). Assume that the bubble does not exchange any heat with the liquid. The bubble contains $n$ moles of gas. The temperature of the gas when the bubble is at the bottom is $T_{0}$ , the height of the liquid is $H$ and the atmospheric pressure is $P_{0}$ (Neglect surface tension).

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1. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

Only the force of gravity
The force due to gravity and the force due

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