Tag: physics

Quizzes (598) Questions (13441)

Questions Related to physics

Multiple choice standing waves waves physics

A standing wave pattern is formed on a string. One of the waves is given by equation  $Y _ { 1 } a \cos ( \omega t - K X + \pi / 3 )$  then the equation of the other wave such at  $X = 0$  a noode is formal

  1. $y _{ 2 } = \operatorname { a sin } \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  2. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
  3. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 2 \pi } { 3 } \right)$
  4. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 4 \pi } { 3 } \right)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a standing wave formed by two waves y1 and y2, if a node exists at x=0, the resultant wave must be zero at x=0 for all t. This requires y1 + y2 = 0 at x=0. Given y1 = a cos(wt - kx + pi/3), at x=0, y1 = a cos(wt + pi/3). Thus, y2 must be -a cos(wt + kx + pi/3), which is equivalent to a cos(wt + kx + pi/3 + pi) = a cos(wt + kx + 4pi/3).

Multiple choice standing waves waves physics

Two simple harmonic waves of amplitude 5 cm and 3 cm and of the same frequency travelling with the same speed in opposite directions superpose to produce stationary waves. The ration of the amplitude at a node to that at an antinode in the resultant wave is

  1. zero

  2. infinity

  3. 5:3

  4. 1:4
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice standing waves waves physics

The equation of stationary wave is given by $y=5\, cos (\pi x/3)\, sin 40 \pi t$ where y and x are given in cm and time t in second. Then a node occurs at the following distance 

  1. 3 cm

  2. 10 cm

  3. 5 cm

  4. 1.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Nodes occur where the spatial part of the stationary wave equation equals zero, meaning cos(pi x / 3) = 0. This happens when pi x / 3 = pi/2, 3pi/2, etc., which yields x = 1.5 cm for the first node. Thus, 1.5 cm is the correct position for a node.

Multiple choice standing waves waves physics

A $string$ is stretched between fixed points separated by $75.0\ cm$. It is observed to have resonant frequencies of $420\ Hz$ and $315\ Hz$. There are no other resonant frequencies between these two.
Then, the lowest resonant frequency for this string is :

  1. $1.05$Hz
  2. $1050$Hz
  3. $10.5$Hz
  4. $105$Hz
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,  $\dfrac { nV }{ 2L } =315\quad \longrightarrow (1)$

     &     $\dfrac { \left( n+1 \right) V }{ 2L } =420\quad \longrightarrow (2)$
equation (2) $-$ equation (1), we get
$\dfrac { \left( n+1 \right) V }{ 2L } -\dfrac { nV }{ 2L } =420-315$
$\Rightarrow \quad \left[ \dfrac { V }{ 2L } =105\quad { H } _{ 3 } \right] \rightarrow $  Lowest possible resonant frequency

$\therefore $  Option (D) is correct.

Multiple choice standing waves waves physics

A wave represented by $y=2 cos (4x-\pi t)$ is superposed with another wave to form a stationary wave such that the point x= 0 is a node. The equation of other wave is:

  1. $2 sin(4x+\pi t)$
  2. $-2 cos (4x -\pi t)$
  3. $-2 cos (4x +\pi t)$
  4. $-2 sin (4x -\pi t)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to options

If $y _2=-2\cos(4x+\pi t)$
Then, when superimposed,
$y=y _1+y _2\ \quad 2\cos(4x-\pi t)-2\cos(4x+\pi t)\ =2[2\sin(\cfrac{(4x-\pi t)+(4x+\pi t)}{2})\sin(\cfrac{(4x-\pi t)-(4x+\pi t)}{2})]\ \quad=2[2\sin(4x)\sin(-\pi t)]\y=-4\sin(4x)\sin(\pi t)$
at $y=0\Rightarrow y=0$ (i.e node)

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The phenomenon in which the amplitude of oscillation of a pendulum decreases gradually is called

  1. decay period of oscillation

  2. damping

  3. building up of oscillation

  4. maintained oscillation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Whenever there is a damping force, it will slow down the motion of a pendulum, and ultimately it will make the pendulum stop. This phenomenon is called damping.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The oscillations of a pendulum slow down due to :

  1. the force exerted by air and the force exerted by friction at the support

  2. the force exerted by air only

  3. the forces exerted by friction at the support

  4. they never slow down
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The pendulum on its motion has friction particle. As a result of this frictional force slows down.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

In which of the following there is some loss of energy in the form of heat

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

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

It is our common experience that when a body is made to vibrate in a medium , the amplitude of the vibrating body continuously decreases with time and ultimately the body stops vibrating.this is called the damped vibrations.

Multiple choice physics free, damped and forced oscillations damped harmonic motion damped oscillation free, forced and damped oscillations

The periodic vibrations of a body of decreasing amplitude in the presence of resistive force on it are called

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

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

Forced vibrations: External force is acting on the body. 
Free vibration: Constant amplitude and no external force.
Damped vibration: Amplitude is not constant, it keeps on decreasing due to environmental factors of the system like air resistance.  
Therefore, correct option is C.