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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.

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.