Tag: superposition of waves-2: stationary (standing) waves: vibrations of air columns

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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

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.

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 strings, the position of antinodes are obtained at

  1. $\lambda,\space2\lambda, \space3\lambda$

  2. $0,\space\lambda,/2 \space\lambda$

  3. $2\lambda,\space4, \space6\lambda$

  4. $\lambda/4,\space3\lambda/4, \space5\lambda/4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a string which is connected at both ends (similarity to sine wave), anti-nodes appear at odd multiples of $\dfrac{\lambda}{4}$.

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 $2\pi f s _{0}\rho V$.