Waves & Oscillations PYQ — Page 13

This question has Statement 1and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again. Statement 2: On filling the arms, the frequency of a tuning fork increases.

The displacement $y(t)=A \sin (\omega t+\phi)$ of a pendulum for $\phi=\frac{2 \pi}{3}$ is correctly represented by

A cylindrical tube, open at both ends, has a fundamental frequency, $\mathrm{f}$, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

A wave represented by the equation $y_1=a \cos$ $(k x-\omega t)$ is superimposed with another wave to form a stationary wave such that the point $x-0$ is node. The equation for the other wave is

Following are expressions for four plane simple harmonic waves (i) $\quad y_1=A \cos 2 \pi\left(n_1 t+\frac{x}{\lambda_1}\right)$ (ii) $y_2=A \cos 2 \pi\left(n_1 t+\frac{x}{\lambda_1}+\pi\right)$ (iii) $y_3=A \cos 2 \pi\left(n_2 t+\frac{x}{\lambda_2}\right)$ (iv) $y_4=A \cos 2 \pi\left(n_2 t-\frac{x}{\lambda_2}\right)$ The pairs of waves which will produce destructive interference and stationary waves respectively in a medium, are

A ring is suspended from a point $S$ on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take $g=\pi^2$ ) 

If a simple pendulum has significant amplitude (up to a factor of $1 / e$ of original) only in the period between $t=0s$ to $t=\tau s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with '$b$' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

An air column in a pipe, which is closed at one end, will be in resonance wtih a vibrating tuning fork of frequency $264 \mathrm{~Hz}$ if the length of the column in $\mathrm{cm}$ is (velocity of sound $=330 \mathrm{~m} / \mathrm{s}$ )

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y=\frac{1}{1+x^2}$ at time $t=0$ and by $y=\frac{1}{\left[1+\left(x-1^2\right)\right]}$ at $t=2 \mathrm{~s}$, where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of wave in $\mathrm{m} / \mathrm{s}$ is

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^2+b t^2+2 \sqrt{a b} x t\right)}$. This represents a

Two particles are executing simple harmonic motion of the same amplitude $\mathrm{A}$ and frequency $\omega$ along the $x$-axis. Their mean position is separated by distance $X_0\left(X_0>A\right)$. If the maximum separation between them is $\left(X_0+A\right)$, the phase difference between their motion is :

A mass $M$, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass $M$ passes through its mean position then a smaller mass $\mathrm{m}$ is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is :

The equation of a wave on a string of linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by $y=0.02(\mathrm{~m}) \sin \left[2 \pi\left(\frac{\mathrm{t}}{0.04(\mathrm{~s})}-\frac{\mathrm{x}}{0.50(\mathrm{~m})}\right)\right]$. The tension in the string is

Three sound waves of equal amplitudes have frequencies $(v-1), v,(v+1)$. They superpose to give beats. The number of beats produced per second will be

If $x, v$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $\mathrm{T}$, then, which of the following does not change with time?

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18 \mathrm{~cm}$ during winter. Repeating the same experiment during summer, she measures the column length to be $\mathrm{xcm}$ for the second resonance. Then

A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005 \cos (\alpha x-\beta t)$. If the wavelength and the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$, respectively, then $\alpha$ and $\beta$ in appropriate units are

The speed of sound in oxygen $\left(\mathrm{O}_2\right)$ at a certain temperature is $460 \mathrm{~ms}^{-1}$. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

A point mass oscillates along the $x$-axis according to the law $\mathrm{x=x_0 \cos (\omega t-\pi / 4)}$. If the acceleration of the particle is written as $\mathrm{a=A \cos (\omega t+\delta)}$

A sound absorber attenuates the sound level by $20 \mathrm{~dB}$. The intensity decreases by a factor of

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2 \times 10^{-2} \cos \pi t$ metres. The time at which the maximum speed first occurs is

Two springs, of force constants $k_1$ and $k_2$, are connected to a mass $\mathrm{m}$ as shown. The frequency of oscillation of the mass is $\mathrm{f}$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes 

A particle of mass $m$ executes simple harmonic motion with amplitude ' $a$ ' and frequency ' $v$ '. The average kinetic energy during its motion from the position of equilibrium to the end is

The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7 \mathrm{~mm}$, is $4.4 \mathrm{~m} / \mathrm{s}$. The period of oscillation is