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

Questions Related to superposition of waves-2: stationary (standing) waves: vibrations of air columns

In a stationary wave, 

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

  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

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Correct Option: A
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.

Standing waves can be produced in.

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

  1. Solid only

  2. Liquid only

  3. Gases only

  4. All of the above

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Correct Option: A
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.

In strings, the position of antinodes are obtained at

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

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

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

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

  4. $\lambda/4,\space3\lambda/4, \space5\lambda/4$

Show answer
Correct Option: D
Explanation:

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

If four loops are formed n a string of length $80$ cm, then the wavelength of stationary wave will be 

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

  1. $0.2$ m

  2. $0.6$ m

  3. $0.8$ m

  4. $0.4$ m

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Correct Option: A

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

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

  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. $a\ quantity\ that\ is\ independent\ of\ the\ properties\ of\ the\ string.$

Show answer
Correct Option: C
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.

Energy is not propogated by:

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

  1. Stationary waves

  2. Electromagnetic waves

  3. Longitudinal progressive waves

  4. transverse progressive waves

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Correct Option: A
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.

Energy is not carried by

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

  1. transverse progressive wave

  2. longitudinal progressive wave

  3. transverse stationary wave

  4. electromagnetic wave

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Correct Option: C
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.

Energy is not carried by which of the following wave?

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

  1. Progressive

  2. Electromagnetic

  3. Transverse

  4. Stationary

Show answer
Correct Option: D
Explanation:

Stationary waves do not carry energy with it as it is stationary or does not change position.

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) $0$
$Y _{1}=a\sin (\omega t-Kx)$
$Y _{2}=a\cos (\omega t-Kx)$

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

  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

Show answer
Correct Option: A
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}$.

Mark incorrect Statement 

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

  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)

Show answer
Correct Option: A,B,C,D
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 $2\pi f s _{0}\rho V$.