Tag: stationary (or standing) waves

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Questions Related to stationary (or standing) waves

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

A standing wave is represented by an equation $y= 20 sin (50 \pi t )cos (10 \pi x)$. The frequency of the wave is

  1. 20 Hz

  2. 50 Hz

  3. 25 Hz

  4. 10 Hz
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equation of a stationary wave is $y= 2A sin \omega t cos K x$. Comparing this equation with the equation given in the problem, we have
$2 \pi f = 50 \implies f = 25 Hz$

The correct option is (c)

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

Which of the following statement is incorrect during propagation of plane progressive mechanical wave?

  1. All the particles are vibrating in the same phase.

  2. Amplitude of all the particles is equal.

  3. Particles of the medium executes SHM.

  4. Wave velocity depends upon the nature of the medium.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

During propagation of a plane progressive mechanical wave all the particles are vibrating with different phases.
While all other statement are correct.

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

A standing wave is given by the equation $x=10 sin 5\pi t cos 3 x$. The amplitude of the wave will be

  1. a constant at all times

  2. will be increasing as t increases

  3. will be decreasing as t increases

  4. will fluctuate at x increases
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The amplitude of the stationary wave is $10 cos 3 x$ and this fluctuates as x increases

The correct option is (d)

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

A standing wave is represented by an equation $y= 10 sin 50 \pi t cos 10 \pi x$. The distance between adjacent nodes of the wave is

  1. 0.5 m

  2. 0.2 m

  3. 0.1 m

  4. 0.3 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At nodes, displacement $y=0$

For first node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { \pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { \pi  }{ 2 } \ x=\cfrac { 1 }{ 20 } $
For second node:
$\cos { \left( 10\pi x \right) =0\quad =\cos { \left( \cfrac { 3\pi  }{ 2 }  \right)  }  } \ \therefore \quad 10\pi x=\cfrac { 3\pi  }{ 2 } \ x=\cfrac { 3 }{ 20 } $
$\therefore$ distance between them $=\cfrac { 3 }{ 20 } -\cfrac { 1 }{ 20 } \ \quad \quad =\cfrac { 1 }{ 10 } =0.1m$

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

The frequency of a sound wave is 250 Hz and its wavelength is 100 cm. The distance travelled by a sound wave in the time taken to produce 100 waves is ________.

  1. 100m

  2. 200m

  3. 300m

  4. 400m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$v = 250 \times 1 = 250  m  s^{-1}$
$t = \displaystyle \frac{100}{250} s = 0.45$
Distance travelled by wave in the time taken to produce 100 waves $=$ v $\times$ time
$= $ 250 $\times$ 0.45
$=112.5m \approx 100m$

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

The waves in which the particles of the medium travel in the same direction as the waves are

  1. linear waves

  2. longitudinal waves

  3. transverse waves

  4. electromagnetic waves
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The waves in which the displacement of the medium is in the same direction as, or the opposite direction to the direction of the propagation of the wave, are called lognitudinal waves. Ex$:-$ Sound waves, sewmic waves

While $:-$ 
The wave in which the displacement of the medium are at right angles to the direction of propogation, are called trensverse waves.
Ex$:-$ Electromagnetic waves, ripple on water surface.
Option (B) is the correct answer

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

Which of the following functions represent a traveling wave ?

  1. $({ x-vt })^{ 2 }$
  2. $({ x-vt })^{ 3 }$
  3. ${ 2 }^{ -(x-vt)^{ 2 } }$
  4. ${ e }^{ (x-vt) }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A traveling wave must be a function of (x - vt) or (x + vt). While A, B, and C are functions of (x-vt), they do not satisfy the wave equation (second derivative in x equals 1/v^2 times second derivative in t) for all physical contexts, but e^(x-vt) is a common form for a traveling wave solution.

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

The equation of the stationary wave is
$y=2A\quad sin(\cfrac { 2\pi ct }{ \lambda  } )cos(\cfrac { 2\pi x }{ \lambda  } )$
Which of the following statement (s) is wrong?

  1. The unit of ct is same as that of $\lambda$
  2. The unit of x is same as that of $\lambda$
  3. The unit of $2\pi t$ is same as that of $2\pi x/\lambda t$
  4. The unit of $c/\lambda$ is same as that of $x/\lambda$
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Explanation

$y=2Asin(\dfrac{2\pi ct}{\lambda}). cos(\dfrac{2\pi x}{\lambda})$


The unit of $\lambda $ and $x$ is $m$


The unit of $ct$ is $m$

The unit of $2\pi t$ is $s$.

The unit of $2\pi x/\lambda t$ is $s^{-1}$

The unit of $\dfrac{c}{\lambda}$ is $s^{-1}$

The unit of $x/\lambda$ is unit less.

The wrong statement is C and D both.

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

In a plane progressive harmonic wave, $V _{P}$ is the maximum particle speed and $V$ is the wave speed. If amplitude of wave is less than $\lambda/ 2\pi$, then

  1. $V = V _{P}$
  2. $V > V _{P}$
  3. $V _{P} < V$

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

Particle speed Vp = A * omega. Wave speed V = omega / k. Vp / V = A * omega / (omega / k) = A * k = A * (2 * pi / lambda). Given A < lambda / (2 * pi), then A * (2 * pi / lambda) < 1, so Vp < V.

Multiple choice physics stationary waves formation of stationary waves stationary waves and its graphical representation standing waves in strings from moving to stationary stationary (or standing) waves

Standing waves are produced in $10m$ long stretched wire. If wire vibrates in five segments and wave velocity is $20m/s$, then the frequency is $(in\ Hz)$

  1. $5$
  2. $10$
  3. $15$
  4. $20$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a wire of length L vibrating in n segments, L = n * lambda / 2. Here L = 10m, n = 5, so 10 = 5 * lambda / 2, lambda = 4m. Frequency f = v / lambda = 20 m/s / 4m = 5 Hz.