JEE Advanced · Physics · 16. Waves & Sound
A transverse sinusoidal wave moves along a string in the positive \(x\)-direction at a speed of \(10 \mathrm{~cm} / \mathrm{s}\). The wavelength of the wave is \(0.5 \mathrm{~m}\) and its amplitude is \(10 \mathrm{~cm}\). At a particular time \(t\), the snap-shot of the wave is shown in figure. The velocity of point \(P\) when its displacement is \(5 \mathrm{~cm}\) is
- A \(\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}\)
- B \(-\frac{\sqrt{3} \pi}{50} \hat{j} \mathrm{~m} / \mathrm{s}\)
- C \(\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\)
- D \(-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Particle velocity \(v_p=-v\) (slope of \(y-x\) graph)
Here,\(v=+v e\), as the wave is travelling in positive \(x\)-direction.
Slope at \(P\) is negative.
\(\therefore\) Velocity of particle is in positive \(y(+\overrightarrow{\mathbf{j}})\) direction.
\(\therefore\) correct option is (a).
Here,\(v=+v e\), as the wave is travelling in positive \(x\)-direction.
Slope at \(P\) is negative.
\(\therefore\) Velocity of particle is in positive \(y(+\overrightarrow{\mathbf{j}})\) direction.
\(\therefore\) correct option is (a).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two batteries of different emfs and different internal resistances are connected as shown. The voltage across \(A B\) in volt is
JEE Advanced 2011 Easy - An electron in a hydrogen atom undergoes a transition from an orbit with a quantum number to another quantum number . are the initial and final potential energies of the electron. If then the smallest isJEE Advanced 2017 Medium
- A disk of radius with uniform positive charge density is placed on the plane with its center at the origin. The Coulomb potential along the -axis is
A particle of positive charge is placed initially at rest at a point on the -axis with and . In addition to the Coulomb force, the particle experiences a vertical force with . Let . Which of the following statement(s) is(are) correct?JEE Advanced 2022 Medium - A block of mass another mass , are placed together (see figure) on an inclined plane with angle of inclination . Various values of are given in List I. The coefficient of friction between the block and the plane is always zero. The coefficient of static and dynamic friction between the block and the plane are equal to . In List II expressions for the friction on the block are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.
[Useful information: ]
List I List II A. B. C. D. JEE Advanced 2014 Medium - A massless rod \(B D\) is suspended by two identical massless strings \(A B\) and \(C D\) of equal lengths. A block of mass ' \(m\) ' is suspended point \(P\) such that \(B P\) is equal to ' \(x\) ', if the fundamental frequency of the left wire is twice the fundamental frequency of right wire, then the value of \(x\) is
JEE Advanced 2006 Hard - Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statement (s) is (are) :JEE Advanced 2013 Medium
More PYQs from JEE Advanced
- Let \(g_{i}:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}, i=1,2\), and \(f:\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right] \rightarrow \mathbb{R}\) be functions such that \(g_{1}(x)=1, g_{2}(x)=|4 x-\pi|\) and \(f(x)=\sin ^{2} x\), for all \(x \in\left[\frac{\pi}{8}, \frac{3 \pi}{8}\right]\)
Define
\[
S_{i}=\int_{\frac{\pi}{8}}^{\frac{3 \pi}{8}} f(x) \cdot g_{i}(x) d x, \quad i=1,2
\]
The value of is ___.JEE Advanced 2021 Medium - Three students \(S_1, S_2\) and \(S_1\) are given a problem to solve. Consider the following events :
\(U:\) At least one of \(S_1, S_2\) and \(S_3\) can solve the problem,
\(V: S_1\) can solve the problem, given that neither \(\mathrm{S}_2\) nor \(\mathrm{S}_3\) can solve the problem,
\(W: S_2\) can solve the problem and \(S_3\) cannot solve the problem,
\(T: S_3\) can solve the problem.
For any event \(E\), let \(P(E)\) denote the probability of \(E\).
If \(P(U)=\frac{1}{2}, P(V)=\frac{1}{10}\) and \(P(W)=\frac{1}{12}\), then \(P(T)\) is equal toJEE Advanced 2025 Medium - Paragraph :
The capacitor of capacitance \(C\) can be charged (with the help of a resistance \(R\) ) by a voltage source \(V\), by closing switch \(S_1\) while keeping switch \(S_2\) open. The capacitor can be connected in series with an inductor \(L\) by closing switch \(S_2\) and opening \(S_1\).
Question :
If the total charge stored in the \(L C\) circuit is \(Q_0\), then for \(t \geq 0\)JEE Advanced 2006 Hard - The value of \(\int_{\sqrt{\log 2}}^{\sqrt{\log 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\log 6-x^2\right)} d x\) isJEE Advanced 2011 Medium
- The correct functional group \(X\) and the reagent/reaction conditions \(Y\) in the following schemes are \(\mathrm{X}-\left(\mathrm{CH}_2\right)_4-X\)
JEE Advanced 2011 Hard - In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength \((\lambda)\) of incident light and the corresponding stopping potential (\(V_0\)) are given below:
Given that \(c=3 \times 10^8 m s^{-1}\) and \(e=1.6 \times 10^{-19} C\), Planck's constant (in units of J s) found from such an experiment is :\(\lambda(\mu m)\) Volt 0.3 2.0 0.4 1.0 0.5 0.4 JEE Advanced 2016 Medium