Tag: formation of stationary waves

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Questions Related to formation of stationary 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

The equation of a stationary wave is given by $ y= 5cos \frac { \pi x }{ 3 }  sin 40 \pi t $. where y and x are given cm and time t in second then the amplitude of the progressive wave is

  1. $2.5 cm$
  2. $10 cm$
  3. $5 cm$
  4. $7.5 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The stationary wave equation is y = 2A * cos(kx) * sin(omega * t). Given y = 5 * cos(...) * sin(...), the amplitude of the stationary wave is 5 cm. The amplitude of the component progressive waves is A = 5 / 2 = 2.5 cm.

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 progressive wave travelling along positive direction of x-axis having an amplitude of $0.04\ m$, frequency $440\ Hz$ and wave velocity $330 m/s$ is

  1. $y = 0.04\sin 2\pi \left (440t - \dfrac {4x}{3}\right )$
  2. $y = 0.04\cos 2\pi \left (440t - \dfrac {3x}{4}\right )$
  3. $y = 0.04\sin 2\pi \left (440t + \dfrac {4x}{3}\right )$
  4. $y = 0.04\cos 2\pi \left (440t + \dfrac {4x}{3}\right )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Wave equation y = A * sin(2 * pi * (ft + x/lambda)) for negative direction or (ft - x/lambda) for positive. Here, positive direction means (ft - x/lambda). f = 440, v = 330, lambda = v/f = 330/440 = 3/4. So 1/lambda = 4/3. Equation: y = 0.04 * sin(2 * pi * (440t - 4x/3)). Note: The option C uses +4x/3 which implies negative direction, but often textbooks use conventions differently. Given the options, C is the closest match.

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 stationary wave

  1. Strain is maximum at nodes

  2. amplitude is minimum at nodes

  3. Strain is maximum at antinodes

  4. Amplitude is zero at all points
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a stationary wave, nodes are points where the displacement is always zero, meaning the amplitude is minimum (zero).

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 plane progressive wave is $100$ Hz. After how much time the same point will be $90^o$ out of phase?

  1. $2.5\times 0^{-3}s$.
  2. $3.5\times 0^{-3}s$.
  3. $4.5\times 0^{-3}s$.
  4. $5.5\times 0^{-3}s$.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$w=2\Pi f$

where f is frequency of wave
Phase angle, $\theta wt$
$90^{\circ}=2\Pi ft$

$t=\dfrac{\Pi }{2\times 2\Pi f}$

$t=\dfrac{1}{4\times 100} $sec

$t=2.5\times 10^{-3}$ sec

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

Progressive wave are waves originating from a source such that they never return to the source.

  1. True

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

progressive waves are waves after generation from the source the keep on propagating on the direction of propagation .

so the answer is A.

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, $Y=0.02 sin (500 \pi t) cos(4.5x)$ represents

  1. progressive wave of frequency 250 Hz along x-axis

  2. a stationary wave of wavelength 1.4 m

  3. a transverse progressive wave of amplitude 0.02 m
  4. progressive wave of speed of about $350ms^{-1} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Comparing the given wave equation with standard standing wave equation
$y (x, t) = A \sin (\omega t)\cos (kx)$, 


we get, $k =4.5$

$k = \dfrac{2\pi}{\lambda}$

$\Rightarrow \lambda = \dfrac{2\pi}{k} =1.4$ $m$

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 a progressive wave is $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$ where x is in metre and t is in second. The velocity of the wave is

  1. $100\pi\,m/s$
  2. $50\pi\,m/s$
  3. $25\pi\,m/s$
  4. $\pi\,m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of the progressive wave is given as, $y=4\,sin(4\pi t-0.04x+\dfrac{\pi}{3})$.

The velocity of the wave would be equal to

$\dfrac{\omega}{k}=\dfrac{4\pi}{0.04}=100\pi\;m/s$

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 statements are correct?

  1. A wave front is a locus of points vibratig in same phase

  2. Wavelength is separation between two consecutive points vibrating in same phase

  3. For two sources to be coherent their frequencies must be same

  4. All of the above statements are correct.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A wavefront is indeed a locus of points in the same phase. Wavelength is the distance between consecutive points in the same phase. Coherent sources must have the same frequency and constant phase difference.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

In a stationary wave, 

  1. Phase is same at all points in a loop

  2. Amplitude is same at all points

  3. Energy is constant at all points

  4. Temperature is same at all points
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let two waves be $y _1=A \sin\ (wt-kx)$
$y _2=A \sin\ (wt+kx)$
$y=y _1+y _2$
$=(2A \cos\ kx)\sin\ wt.$ 
For all point in one loop i.e as $x$ varies in $2A \cos k x$, the phase is same. The phase changes only after crossing a node.

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns from moving to stationary stationary (or standing) waves formation of stationary waves

Standing waves can be produced in.

  1. Solid only

  2. Liquid only

  3. Gases only

  4. All of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Standing wave produces when two waves of identical frequency interfere with one another while travelling in opposite directions and this coincidence directions and this coincidence is not possible in fluids or gases.