1
JEE Advanced 2024 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

Two uniform strings of mass per unit length $\mu$ and $4 \mu$, and length $L$ and $2 L$, respectively, are joined at point $\mathrm{O}$, and tied at two fixed ends $\mathrm{P}$ and $\mathrm{Q}$, as shown in the figure. The strings are under a uniform tension $T$. If we define the frequency $v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$, which of the following statement(s) is(are) correct?

A
With a node at $\mathrm{O}$, the minimum frequency of vibration of the composite string is $v_0$.
B
With an antinode at $\mathrm{O}$, the minimum frequency of vibration of the composite string is $2 v_0$.
C
When the composite string vibrates at the minimum frequency with a node at $\mathrm{O}$, it has 6 nodes, including the end nodes.
D
No vibrational mode with an antinode at $\mathrm{O}$ is possible for the composite string.
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and f0 is the fundamental frequency of the pipe. For which of the following combination(s) of u and fs, will the sound reaching the pipe lead to a resonance?
A
u = 0.8v and fs = f0
B
u = 0.8v and fs = 2f0
C
u = 0.8v and fs = 0.5f0
D
u = 0.5v and fs = 1.5f0
3
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $$500$$ $$Hz$$ is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length $$50.7$$ $$cm$$ and $$83.9$$ $$cm.$$ Which of the following statements is (are) true?
A
The speed of second determined from this experiment is $$332\,m{s^{ - 1}}$$
B
The end correction in this experiment is $$0.9$$ $$cm$$
C
The wavelength of the sound wave is $$66.4$$ $$cm$$
D
The resonance at $$50.7$$ $$cm$$ corresponds to the fundamental harmonic
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A block $$M$$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigid support at $$O.$$ A transverse wave pulse (Pulse 1) of wavelength $${\lambda _0}$$ is produced at point $$O$$ on the rope. The pulse takes time $${T_{OA}}$$ to reach point $$A.$$ If the wave pulse of wavelength $${\lambda _0}$$ is produced at point $$A$$ (Pulse 2) without disturbing the position of $$M$$ it takes time $${T_{AO}}$$ to reach point $$O.$$ which of the following options is/are correct?

A
The time $${T_{AO}} = {T_{OA}}$$
B
The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
C
The wavelength of Pulse 1 becomes longer when it reaches point $$A$$
D
The velocity of any pulse along the rope is independent of its frequency and wavelength
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