Tag: time period, frequency and amplitude of sound

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Questions Related to time period, frequency and amplitude of sound

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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. $A\left( {\dfrac{{M + m}}{m}} \right)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a forced oscillation problem. The equation of motion is x'' + 4x = sin(t). The particular solution is of the form x = C*sin(t). Plugging in: -C*sin(t) + 4*C*sin(t) = sin(t) => 3C = 1 => C = 1/3. The general solution includes the homogeneous part A*sin(2t) + B*cos(2t). Matching initial conditions leads to the correct form.

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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. $y = - 4 \tan ( \alpha x - k x )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A progressive wave traveling in the positive x-direction is represented by a function of (wt - kx).

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation x = 2*sin(wt) + 3*sin^2(wt) can be written as 2*sin(wt) + 1.5*(1 - cos(2wt)). This is a sum of two periodic functions with different frequencies, so the motion is periodic and oscillatory, but not SHM because it is not a single sine/cosine term.

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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. $0.1 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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. $y= a\tan\omega t$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

SHM requires a restoring force proportional to displacement, resulting in a sine or cosine function of time. Tangent functions do not represent SHM.

Multiple choice physics sound: production of sound oscillation - amplitude, time period and frequency of oscillation time period, frequency and amplitude of sound oscillatory and periodic motion

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

  1. more than three

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
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.