Tag: time period, frequency and amplitude of sound

Questions Related to time period, frequency and amplitude of sound

A block of mass $M$ is performing $SHM$ with amplitude $A$ on a smooth horizontal surface$.$ At the extreme position a small block of mass $m$ falls vertically and sticks to$M.$ then$,$ amplitude of oscillation will be                                               

  1. $A$

  2. $A\sqrt {\dfrac{M}{{M + m}}} $

  3. $A\left( {\dfrac{M}{{M + m}}} \right)$

  4. $A\left( {\dfrac{{M + m}}{m}} \right)$


Correct Option: B

A simple harmonic oscillator of angular frequency $2$ rad/s is acted upon by an external force $F = \sin t$ N. If the oscillator is at rest in its equilibrium position at $t= 0$, its position at later times is proportional to:

  1. $ \sin t + \cfrac{1}{2} \cos 2t$

  2. $ \cos t - \cfrac{1}{2} \sin 2t$

  3. $ \sin t + \cfrac{1}{2} \sin 2t$

  4. $ \sin t - \cfrac{1}{2} \sin 2t$


Correct Option: D

Select proper wave equation which describes simple harmonic progressive wave travelling along positive $X$ axis.

  1. $y = A \sin ( \alpha t + k x )$

  2. $y = A \cos ( o t + k x )$

  3. $y = A \sin ( a t - k x )$

  4. $y = - 4 \tan ( \alpha x - k x )$


Correct Option: C

The motion represented by equation $x=2\sin \omega t+3\sin^{2}\omega t$ is

  1. Periodic

  2. Oscillatory

  3. $SHM$

  4. Both (1) & (2)


Correct Option: B

A particle of mass $0.1 kg$ executes SHM under a force $F = (-10 x) N$. Speed of particle at mean position is $6 m/s$. Then amplitude of oscillations is 

  1. $0.6 m$

  2. $0.2 m$

  3. $0.4 m$

  4. $0.1 m$


Correct Option: A
Explanation:

$\begin{array}{l} M=0.1\, Kg \ f=-10x \ \Rightarrow k=10 \ w=\sqrt { \frac { k }{ m }  }  \ =\sqrt { \frac { { 10 } }{ { 0.1 } }  } =10 \ { V _{ \max   } }=6m/s \ \Rightarrow A=\frac { 6 }{ { 10 } } =0.6m \ Hence,\, the\, option\, A\, is\, the\, correct\, answer. \end{array}$

Select the correct statements.

  1. A simple harmonic motion is necessarily periodic.

  2. A simple harmonic motion is necessarily oscillatory.

  3. An oscillatory motion is necessarily periodic.

  4. A periodic motion is necessarily oscillatory.


Correct Option: A,B,D

Equation of SHM is $x=10\sin{10\pi t}$. Find the distance between the two points where speed is $50\pi$ $cm/sec$. $x$ is in cm and $t$ is in seconds

  1. $10cm$

  2. $20cm$

  3. $17.32cm$

  4. $8.66cm$


Correct Option: D

Which of the following equation does not represent a simple harmonic motion:

  1. $y=a\sin\omega t$

  2. $y=b\cos\omega t$

  3. $y=a\sin\omega t+b\cos\omega t$

  4. $y= a\tan\omega t$


Correct Option: D

What is the number of degrees of freedom of an oscillating simple pendulum?

  1. more than three

  2. 3

  3. 2

  4. 1


Correct Option: C
Explanation:

There are 2 degrees of freedom, 1 translational along which the pendulum bob moves, and second rotational - the hinge about which it forms an arc motion.

All oscillatory motions are ______

  1. periodic

  2. linear

  3. rotatory

  4. curvilinear


Correct Option: A
Explanation:

All oscillatory is periodic, as in all oscillatory motion particle repeats its position after a certain interval of time.