Every question from past board papers on Oscillations and Waves, newest paper first. Open any question for its full worked answer.
In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency \(\omega(t)\) and average amplitude \(A(t)\) of the system change with time \(t\). Which one of the following options schematically depicts these changes correctly?
Two identical point masses P and Q, suspended from two separate massless springs of spring constants \(k_1\) and \(k_2\), respectively, oscillate vertically. If their maximum speeds are the same, the ratio (\(A_Q/A_P\)) of the amplitude \(A_Q\) of mass \(Q\) to the amplitude \(A_P\) of mass \(P\) is:
A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :
If \(x=5\sin\left(\pi t+\frac{\pi}{3}\right)m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are :
If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is \(\frac{x}{2}\) times its original time period. Then the value of \(x\) is:
The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is :
The \(x\)-\(t\) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at \(t=2\) s is :
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :
Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :
A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is :
A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is :
The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :
In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be :
The displacement of a particle executing simple harmonic motion is given by
\(y = A_0 + A\sin\omega t + B\cos\omega t\).
Then the amplitude of its oscillation is given by :
Average velocity of a particle executing SHM in one complete vibration is :
The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig.
\(y\)-projection of the radius vector of rotating particle P is :
The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is
A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m/s\(^2\) at a distance of 5 m from the mean position. The time period of oscillation is
Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s] :
The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system ?
A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is :
A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is :
A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of \(15\ ms^{-1}\). Then, the frequency of sound that the observer hears in the echo reflected from the cliff is : (Take velocity of sound in air \(= 330\ ms^{-1}\))
A uniform rope of length L and mass \(m_1\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\lambda_2/\lambda_1\) is :
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is :
A body of mass \(m\) is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass \(m\) is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass \(m\) is increased by 1 kg, the time period of oscillations becomes 5 s. The value of \(m\) in kg is
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe \(L\) metre long. The length of the open pipe will be
Three sound waves of equal amplitudes have frequencies \((n-1)\), \(n\), \((n+1)\). They superimpose to give beats. The number of beats produced per second will be
