Tag: physics

Questions Related to 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

standing waves waves physics

  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. $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 4 \pi } { 3 } \right)$

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Correct Option: D

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

standing waves waves physics

  1. zero

  2. infinity

  3. 5:3

  4. 1:4

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Correct Option: A

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 

standing waves waves physics

  1. 3 cm

  2. 10 cm

  3. 5 cm

  4. 1.5 cm

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Correct Option: A

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 :

standing waves waves physics

  1. $1.05$Hz

  2. $1050$Hz

  3. $10.5$Hz

  4. $105$Hz

Show answer
Correct Option: D
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.

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:

standing waves waves physics

  1. $2 sin(4x+\pi t)$

  2. $-2 cos (4x -\pi t)$

  3. $-2 cos (4x +\pi t)$

  4. $-2 sin (4x -\pi t)$

Show answer
Correct Option: C
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)

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

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

  1. decay period of oscillation

  2. damping

  3. building up of oscillation

  4. maintained oscillation

Show answer
Correct Option: B
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.

The oscillations of a pendulum slow down due to :

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

  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

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Correct Option: A
Explanation:

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

Vibrations, whose amplitudes of oscillation decrease with time, are called :

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

  1. free vibrations

  2. forced vibrations

  3. damped vibrations

  4. sweet vibrations

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Correct Option: C
Explanation:

In case of dumped vibrations amplitude of oscillation gradually decreases with time.

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

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

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All

Show answer
Correct Option: C
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.

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

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

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All

Show answer
Correct Option: C
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.