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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

Equation of a standing wave is expressed as $y=2A\sin { \omega t } \cos { kx } $. In the equation, quantity $\omega /k$ represents 

  1. $the\ transverse\ speed\ of\ the\ particles\ of\ the\ string.$

  2. $the\ speed\ of\ the\ component\ waves.$

  3. $the\ speed\ of\ the\ standing\ wave.$

  4. $a\ quantity\ that\ is\ independent\ of\ the\ properties\ of\ the\ string.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equ of standing wave is $y=2A \sin wt \cos Kx$. The quantity $\dfrac { W }{ K } $ always represent the speed of the wave.


Hence Option (C) is correct.

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

Energy is not propogated by:

  1. Stationary waves

  2. Electromagnetic waves

  3. Longitudinal progressive waves

  4. transverse progressive waves
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Stationary wave is also known as standing wave. It remains in a constant position. Two opposing waves combine to form a standing wave. Hence energy is not propagated in stationary wave.

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

Energy is not carried by

  1. transverse progressive wave

  2. longitudinal progressive wave

  3. transverse stationary wave

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

The main difference between stationary and progressive waves is: Progressive waves transfer energy from one place to another, without transferring matter and Stationary waves do not transfer energy from one place to another. Clearly only one option has stationary waves.

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

List - I                                                        List - II
a)  Phase difference                                 e) $\pi $
between two particles in
 alternate loops.
b)  Phase difference                                 f)  $\displaystyle \frac{\pi}{2}$
 between two particles in
successive loops
c)  Phase difference between                g) $2\pi $
two particles in the same loop
d)  Phase difference between                h) $0$
$Y _{1}=a\sin (\omega t-Kx)$
$Y _{2}=a\cos (\omega t-Kx)$

  1. a-g, b-e, c-h, d-f

  2. a-e, c-f, d-g, e-h

  3. a-f, b-e, c-g, d-h

  4. a-g, b-e, c-f, d-h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

a ) Two particles in alternate loops refers to particles having same phase and direction
$\therefore $ phase difference is $2\pi $
b ) Two particles in successive loops differs in phase by $\pi $ 
c ) Two particles in same loop are always in phase $\Rightarrow $ phase difference is $0$.
d ) $y _1= a  \sin  (\omega t-kx)$
$y _2= a  \cos  (\omega t-kx)$
$= a  \sin (\omega t-kx +\dfrac{\pi}{2})$
$\Rightarrow $ phase difference is $ \dfrac{\pi }{2}$.

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

Mark incorrect Statement 

  1. Magnitude of strain is maximum at antinode because medium particles at antinodes have maximum possible velocity

  2. Nodes and antinodes form in case of stationary waves only.

  3. In case of stationary waves maximum pressure change occurs at antinode.

  4. Due to propagation of longitudinal wave in air maximum pressure change is equal to $\dfrac{2\pi fs _{0}}{\rho v}.$ ($f$ : frequency, $s _{0}$ : maximum displacement, $\rho$ : density of medium, $v $: speed of wave)
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

(A) Magnitude of strain is maximum at antinode because medium particles at antinodes have minimum possible velocity.
(B) Nodes and antinodes form in case of travelling waves also.
(C) In case of stationary waves maximum pressure change occurs at node.
(D) Due to propagation of longitudinal wave in air maximum pressure change is equal to $2\pi f s _{0}\rho V$.

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

Assertion - In a stationary wave, no transfer of energy takes place.
Reason - There is no onward motion of the disturbance from one particle to adjoining particle in stationary wave.

  1. Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

  3. Assertion is correct but Reason is incorrect

  4. Both Assertion and Reason are incorrect
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In stationary wave, total energy associated with it is twice the energy of each of incident and reflected wave. large amount of energy are stored equally in standing wave and became trapped with wave. Hence there is no transmission of energy through the waves.

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

As two students holds opposite ends of slinky that is the resting on the floor, one student shakes the end he is holding back and forth with the constant frequency. He later shakes exactly the same way but with a much greater frequency.
Which statement best describes other changes that take place as a result of this increased frequency?

  1. The wave speed and the wavelength both increases.

  2. The wave speed increases, but the wavelength does not significantly change.

  3. The wavelength increases ,but the wave speed does not significantly change.

  4. The wave speed decreases, but the wavelength does not significantly change.

  5. The wavelength decreases ,but the wave speed does not significantly change.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that frequency of a wave is characterized by the source of wave . In both the cases wave in the slinky has a constant frequency but not same in both cases  , 

now we have $v=f\lambda$ ,
or                  $f=v/\lambda$ , 
when frequency $f$ is  increased in second case , wave speed $v$ increases and to maintain a constant frequency $f$ (to maintain a constant ratio), wavelength $\lambda$ also increases
 .

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 standing wave on a string.

  1. In one time period all the particles are simultaneously at rest twice.

  2. All the particles must be at their positive extremes simultaneously once in one time period.

  3. All the particles may be at their positive extremes simultaneously once in a time period.

  4. All the particles are never at rest simultaneously.
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Standing waves are obtained when two waves with same angular frequencies and velocity are superimposed, (They are however moving in the opposite directions).
$x(t) = A\sin(\omega t - kx) + A\sin(\omega t + kx + \delta)$
$x(t) = 2A\cos(kx)\sin(\omega t +\dfrac{\delta}{2})$
For all particles to be simultaneously at rest, the value of the sine function must be equal to zero.
i.e. $\omega t + \dfrac{\delta}{2} = n\pi$
$\Rightarrow$ $t = \dfrac{1}{\omega}(n\pi - \dfrac{\delta}{2})$
$\omega = \dfrac{2\pi}{T}$
$\Rightarrow$ $t = \dfrac{T}{2\pi}(n\pi - \dfrac{\delta}{2})$
$t _{1} =  \dfrac{T}{2\pi}(n\pi - \dfrac{\delta}{2})$
$t _{2} =  \dfrac{T}{2\pi}((n+1)\pi - \dfrac{\delta}{2})$
$t _{2} - t _{1} = \dfrac{T}{2}$


So, the time between this event happening twice is half to time period, so in one cycle this would happen twice. So Option (A)
For the particle to be at positive extreme the sine function can take a value of 1 only.
It can be shown that this happens at an interval of '$T$'
So it will happen twice in a time period if the displacement is max at the start of the time period and once more at the end of the time period,
or else it would happen only once in a time period. Hence Option (C)