Tag: waves

Quizzes (32) Questions (233)

Questions Related to waves

Multiple choice standing waves waves physics

Which of the following function represent traveling waves?

  1. $ y = (x + 5t)^3 $
  2. $ y = tan (2x + 3t) $
  3. $ y = \theta^{(4t+2x)^2} $
  4. $ y = \frac { 1 }{ x + 3t } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A function represents a traveling wave if it can be written in the form f(ax +/- bt). Option D, y = 1/(x + 3t), fits this form, representing a wave traveling in the negative x-direction.

Multiple choice standing waves waves physics

A progressive wave is incident normally on a flat reflector. The reflected wave overlaps with the incident wave and a stationary wave is formed.
At an antinode, what could be the ratio $\dfrac{displacement of the incident wave}{displacement of the reflected wave}$ at any instant?

  1. $-1$
  2. $0$
  3. $1$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standing wave is formed when two waves with equal magnitude and and opposite direction overlap Both waves have same amplitude at antinode and opposite amplitude at node.

Multiple choice standing waves waves physics

A travelling wave represented by y = A  $\sin { \left( \omega t-kx \right)  } $ is superimposed on another wave represented by y = A $\sin { \left( \omega t+kx \right)  } $. The resultant is:

  1. A standing wave having nodes at X = $\dfrac { v\lambda }{ 2 } $;n = 0,1,2,..................
  2. A standing wave have nodes at X=$\left( n+\dfrac { 1 }{ 2 } \right) \dfrac { \lambda }{ 2 } $;n = 0,1,2,...............................

  3. A wave travelling along +x direction.

  4. A wave travelling along -x direction
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Intensity wave is standing wave and have nodes at 
$X=\left( n+\dfrac { 1 }{ 2 }  \right) \dfrac { \lambda  }{ 2 } $ n=0,1,2,......

Multiple choice standing waves waves physics

A sine wave described by the equation $x = 2 sin (2 \pi t-3 x)$ is progressing along an x axis. In order that a standing wave is setup, what should be the equation of the reflected wave

  1. $x = 2 sin (2 \pi t-3 x)$
  2. $x = 2 sin (2 \pi t+3 x)$
  3. $x = 2 sin (2 \pi t-3 x+ \pi)$
  4. $x = 2 sin (2 \pi t-3 x+\pi/3)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since the reflected wave differs from the incident wave by two aspects (direction of the wave and the phase of the wave), the wave will have an equation given by $x = 2 sin (2 \pi t-3 x +\pi)$ to form a stationary wave

The correct option is (c)

Multiple choice standing waves waves physics

A string attached to a tuning fork of frequency 300 Hz is made to vibrate. The other end of the string is fixed to a wall. If stationary waves are to be set up, what should be the phase of the reflected wave

  1. $\pi $ rads
  2. $\pi/2 $ rads
  3. $\pi/3 $ rads

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The reflected and the actual wave has to be out of phase and only in such cases, a stationary wave is being setup

The correct option is (a)

Multiple choice standing waves waves physics

Two sine waves of same frequency (f) and amplitude (A) are superimposed from opposite directions along a straight line. The resultant wave will have an amplitude of 

  1. A

  2. A/2

  3. 2A

  4. 3A/2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Their amplitudes get doubled

The correct option is (c)

Multiple choice standing waves waves physics

A traveling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and  

  1. The wavelength is 5 m

  2. The frequency is 5 Hz

  3. The velocity of propagation is 5 m/s

  4. The wavelength is 0.2 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The frequency is $5Hz$


Phase difference,

$\Delta \phi =\dfrac{2\pi}{T}(\Delta t)$

$2\pi =\dfrac{2\pi}{T}(0.2)$

$\Rightarrow \dfrac{1}{T}=5 sec^{-1}$

$n=5Hz$

Multiple choice standing waves waves physics

A string is vibrating in $n$ loops. The number of nodes and antinodes respectively are

  1. $n, n$
  2. $(n+1), n$
  3. $n, (n-1)$
  4. $(n-1), n$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a string vibrating in n loops, the points where the string does not move are nodes, and the points of maximum displacement are antinodes. For n loops, there are n+1 nodes (including the ends) and n antinodes.

Multiple choice standing waves waves physics

An organ pipe of length $80\ cm$ is opened at $x=0$ and closed at $x=80\ cm$. Speed of sound in the air column is $320\ m/sec$. If standing waves are generated in the closed organ pipe, then the correct equation of standing waves is/are (Here $s=$ longitudinal displacement, $P _{ex}=$ pressure excess) (Neglect the end correction).

  1. $S=A\cos\left(\dfrac{5\pi}{4}x\right)\sin\left(400\pi t\right)$
  2. $S=A\cos\left(\dfrac{5\pi}{8}x\right)\cos\left(1000\pi t\right)$
  3. $P _{ex}=A\cos\left(\dfrac{5\pi}{8}x\right)\sin\left(200\pi t\right)$
  4. $P _{ex}=A\sin\left(\dfrac{25\pi}{8}x\right)\cos\left(1000\pi t\right)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a pipe closed at one end (x=L) and open at the other (x=0), the pressure excess P_ex is zero at the open end (node) and maximum at the closed end (antinode). The standing wave equation for pressure is P_ex = A cos(kx) sin(wt). Given L=0.8m and v=320m/s, the fundamental frequency is v/4L = 100 Hz, so w = 200 pi. k = w/v = 200 pi / 320 = 5 pi / 8.

Multiple choice standing waves waves physics

Consider single slit experiment of diffraction of light. If light of wavelength $5000\ \mathring { A } $ fall on a slit of width $1\mu\ m$ then the angular width of central maximum. 

  1. ${30}^{o}$
  2. ${15}^{o}$
  3. ${60}^{o}$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer