Waves & Oscillations PYQ — Page 4

Each of the two strings of length $51.6 \mathrm{~cm}$ and $49.1 \mathrm{~cm}$ are tensioned separately by $20 \mathrm{~N}$ force. Mass per unit length of both the strings is same and equal to $1 \mathrm{~g} / \mathrm{m}$. When both the strings vibrate simultaneously the number of beats is :

A wave in a string has an amplitude of $2 \mathrm{~cm}$. The wave travels in the +ve direction of $\mathrm{x}$-axis with a speed of $128 \mathrm{~m} / \mathrm{s}$ and it is noted that 5 complete waves fit in $4 \mathrm{~m}$ length of the string. The equation describing the wave is

Which one of the following equations of motion represents simple harmonic motion?

Each of the two strings of length $51.6 \mathrm{~cm}$ and $49.1 \mathrm{~cm}$ are tensioned separately by $20 \mathrm{~N}$ force. Mass per unit length of both the strings is same and equal to $1 \mathrm{gm}^{-1}$. When both the strings vibrate simultaneously the number of beats is

A wave in a string has an amplitude of $2 \mathrm{~cm}$. The wave travels in the +ve direction of $x$ axis with a speed of $128 \mathrm{~ms}^{-1}$ and it is noted that 5 complete waves fit in $4 \mathrm{~m}$ length of the string. The equation describing the wave is

A point performs simple harmonic oscillation of period $T$ and the equation of motion is given by $x=a \sin (\omega t+ \frac{\pi}{6})$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

. Two points are located at a distance of $10 \mathrm{~m}$ and $15 \mathrm{~m}$ from the source of oscillation. The period of oscillation is $0.05 \mathrm{sec}$ and the velocity of the wave is $300 \mathrm{~m} / \mathrm{sec}$. What is the phase difference between the oscillations of two points?

Two Simple Harmonic Motions of angular frequency 100 and $1000 \mathrm{rad} \mathrm{s}^{-1}$ have the same displacement amplitude. The ratio of their maximum accelerations is

The wave described by $y=0.25 \sin (10 \pi x-2 \pi t)$, where $x$ and $y$ are in metre and $t$ in second, is a wave travelling along the

Two points are located at a distance of $10 \mathrm{~m}$ and $15 \mathrm{~m}$ from the source of oscillation. The period of oscillation is $0.05 \mathrm{~s}$ and the velocity of the wave is $300 \mathrm{~m} / \mathrm{s}$. What is the phase difference between the oscillations of two points?

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

The wave described by $y=0.25 \sin (10 \pi x-2 \pi t)$, where $\mathrm{x}$ and $\mathrm{y}$ are in meters and $\mathrm{t}$ in seconds, is a wave travelling along the

A point performs simple harmonic oscillation of period $\mathrm{T}$ and the equation of motion is given by $x=a \sin (w t+\pi / 6)$. After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

Two simple harmonic motions of angular frequency 100 rad/s and 1000 rad/s have the same displacement amplitude. The ratio of their maximum acceleration is

A mass of $2.0 \mathrm{~kg}$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is $200 \mathrm{~N} / \mathrm{m}$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take $g=10 \mathrm{~m} / \mathrm{s}^2$ ). 

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is :

The particle executing simple harmonic motion has a kinetic energy $K_0 \cos ^2$ $\omega t$. The maximum values of the potential energy and the total energy are respectively.

A particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is $T$. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

Which one of the following statements is true?

A transverse wave propagating along $x$-axis is represented by $y(x, t)=8.0$ $\sin (0.5 \pi x-4 \pi t-\pi / 4)$ where $x$ is in metres and $t$ is in seconds. The speed of the wave is:

Two sound waves with wavelengths 5.0 $\mathrm{m}$ and $5.5 \mathrm{~m}$ respectively, each propagate in a gas with velocity $330 \mathrm{~m} / \mathrm{s}$. We expect the following number of beats per second:

The time of reverberation of a room $\mathrm{A}$ is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room $\mathrm{A}$ ?

A point source emits sound equally in all directions in a non-absorbing medium. Two points $\mathrm{P}$ and $\mathrm{Q}$ are at distances of 2 $\mathrm{m}$ and $3 \mathrm{~m}$ respectively from the source. The ratio of the intensities of the wave at $P$ and $Q$ is: