List of top Physics Questions on Waves and Oscillations asked in IIT JAM PH

Identify which of the following wave functions describe(s) travelling wave(s).
(\(A_0, B_0, a\), and \(b\) are positive constants of appropriate dimensions)
Consider the superposition of two orthogonal simple harmonic motions \(y_1 = a \cos 2\omega t\) and \(y_2 = b \cos(\omega t + \phi)\). If \(\phi = \pi\), the resultant motion will represent
(a, b and \(\omega\) are constants with appropriate dimensions)
A whistle S of sound frequency f is oscillating with angular frequency πœ” along the x-axis. Its instantaneous position and the velocity are given by π‘₯(𝑑) = π‘Ž sin(πœ”π‘‘) and 𝑣(𝑑)=𝑣0 cos (πœ”π‘‘), respectively. An observer P is located on the y-axis at a distance L from the origin (see figure). Let 𝑣𝑃𝑆(𝑑) be the component of 𝑣(𝑑) along the line joining the source and the observer. Choose the correct option(s):
(Here π‘Ž and 𝑣0 are constants)
A whistle S of sound frequency f
If two traveling waves, given by
𝑦1=𝐴0 sin(Ξ±π‘˜π‘₯ -πœ”π‘‘) and 𝑦2=𝐴0 sin(Ξ±π‘˜π‘₯ βˆ’ Ξ²πœ”π‘‘) 
are superposed, which of the following statements is correct?
Which of the following types of motion may be represented by the trajectory,
𝑦(π‘₯)=π‘Žπ‘₯ 2+𝑏π‘₯+𝑐 ? 
(Here a, b, and c are constants; x, y are the position coordinates)
A particle moving along the x-axis approaches π‘₯=0 from π‘₯ =βˆ’βˆž with a total energy E. It is subjected to a potential 𝑉(π‘₯). For time π‘‘β†’βˆž, the probability density P(x) of the particle is schematically shown in the figure.
A particle moving along the x-axis
The correct option for the potential 𝑉(π‘₯) is:
A periodic function f(x) = x2 for -Ο€ < x < Ο€ is expanded in a Fourier series. Which of the following statement(s) is/are correct ?
A uniform stick of length l and mass m pivoted at its top end is oscillating with an angular frequency Ο‰r . Assuming small oscillations, the ratio Ο‰r/Ο‰s , where Ο‰s is the angular frequency of a simple pendulum of the same length, will be
A single pendulum hanging vertically in an elevator has a time period 𝑇0 when the elevator is stationary. If the elevator moves upward with an acceleration of π‘Ž = 0.2𝑔, the time period of oscillations is 𝑇1. Here 𝑔 is the acceleration due to gravity. The ratio\( \frac{𝑇_0}{ 𝑇_1}\) is (rounded off to two decimal places).
A particle is subjected to two simple harmonic motions along the x and y axes, described by x(t) = \(\alpha\)sin(2\(\omega\)t + Ο€) and y(t) = 2\(\alpha\) sin(\(\omega\)t). The resultant motion is given by
A particle is executing simple harmonic motion with time period T. Let x, v an a denote the displacement, velocity and acceleration of the particle, respectively- at time t. Then,
Two transverse waves \(y_1 = 5 \cos(kx - \omega t)\) cm and \(y_2 = 5 \cos(kx + \omega t)\) cm, travel on a string along the x-axis. If the speed of a point at \(x = 0\) is zero at \(t = 0\,s,\ 0.25\,s,\) and \(0.5\,s,\) then the minimum frequency of the waves is ............ Hz.
An object executes simple harmonic motion along the x-direction with angular frequency \(\omega\) and amplitude \(a\). The speed of the object is 4 cm/s and 2 cm/s when it is at distances 2 cm and 6 cm, respectively, from the equilibrium position. Which of the following is/are correct?
Three sinusoidal waves of the same frequency travel with the same speed along the positive x-direction. The amplitudes of the waves are \(a, a/2, a/3\), and the phase constants of the waves are \(\pi/2, \pi, 3\pi/2\), respectively. If \(A_m\) and \(\phi_m\) are the amplitude and phase constant of the wave resulting from the superposition of the three waves, which of the following is/are correct?

Two vehicles A and B are approaching an observer O at rest with equal speed as shown in the figure. Both vehicles have identical sirens blowing at a frequency $f_s$. The observer hears these sirens at frequency $f_A$ and $f_B$, respectively. Which one of the following is correct? 

A particle of mass $m$ moves in the positive $x$ direction under the potential $V(x)=\frac{1}{2}kx^{2}+\frac{\lambda}{2x^{2}}$. If the particle is slightly displaced from equilibrium, the angular frequency $\omega$ is ............... (Give answer in units of $\sqrt{k/m}$ as an integer.)
 

Consider two waves $y_1=a\cos(\omega t-kz)$ and $y_2=a\cos[(\omega+\Delta \omega)t-(k+\Delta k)z]$. The group velocity of the superposed wave will be ($\Delta \omega \ll \omega$ and $\Delta k \ll k$)
For a proton to capture an electron to form a neutron and a neutrino (assumed massless), the electron must have some minimum energy. For such an electron, the de Broglie wavelength in picometers is: