Tag: waves

Quizzes (32) Questions (233)

Questions Related to waves

Multiple choice standing waves waves physics

The equation of a traveling and stationary wave are ${ y } _{ 1 }=a sin(\omega t-kx)$ and ${ y } _{ 2 }=a \sin kx  \cos \omega t$. The phase difference between two point ${ x } _{ 1 }=\dfrac { \pi  }{ 4k }$ and $ { x } _{ 2 }=\dfrac { 4\pi  }{ 3k } $ are ${ \phi  } _{ 1 }$ and ${ \phi  } _{ 2 }$ respectively for two waves where k is the wave number, the ratio of ${ \phi  } _{ 1 }/{ \phi  } _{ 2 }$ 

  1. 6/7

  2. 16/3

  3. 12/13

  4. 13/12
Reveal answer Fill a bubble to check yourself
D Correct answer
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 energy in wave motion oscillation and waves waves physics

If the energy density and velocity of a wave are $u$ and $c$ respectively then the energy propagating per second per unit area will be

  1. $u/c$
  2. $c^2u$
  3. $uc$
  4. $c/u$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the energy density and velocity of a wave are $u$ and $c$ respectively then the energy propagating per second per unit area will be $uc.$

Multiple choice energy in wave motion oscillation and waves waves physics

The kinetic energy per unit length for a wave on a string is the positional coordinate

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The kinetic energy for a particle is given by $(\mu \Delta x/ 2) (\dfrac{dy}{dt})^2$

Thus, it depends only on the time variable and not on the position variable

Multiple choice energy in wave motion oscillation and waves waves physics

A travelling wave has an equation of the form $A(x,t)=f(x+vt)$. The relation connecting positional derivative with time derivative of the function is:

  1. $\dfrac{dA}{dt}=\pm v^2 \dfrac {dA}{dx}$
  2. $\dfrac{dA}{dt}=\pm v \dfrac {dA}{dx}$
  3. $\dfrac{dA}{dt}=\pm \sqrt(v) \dfrac {dA}{dx}$
  4. $\dfrac{dA}{dt}=(2 \pi v/\lambda) \dfrac {dA}{dx}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Positional derivative and time derivative of a function f is $\dfrac{dA}{dt}=\pm v \dfrac {dA}{dx}$

The correct option is (b)

Multiple choice energy in wave motion oscillation and waves waves physics

Kinetic energy per unit length for a particle in a standing wave is zero at:

  1. nodes

  2. antinodes

  3. mid-way between a node and an antinode

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Particle at antinodes is momentarily at rest and hence has zero kinetic energy. Its speed comes down to zero at this point and all energy is stored in the form of potential energy.