Questions
Which of the following function represent traveling waves?
- $ y = (x + 5t)^3 $
- $ y = tan (2x + 3t) $
- $ y = \theta^{(4t+2x)^2} $
- $ y = \frac { 1 }{ x + 3t } $
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?
- $-1$
- $0$
- $1$
- $2$
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:
- A standing wave having nodes at X = $\dfrac { v\lambda }{ 2 } $;n = 0,1,2,..................
- A standing wave have nodes at X=$\left( n+\dfrac { 1 }{ 2 } \right) \dfrac { \lambda }{ 2 } $;n = 0,1,2,...............................
- A wave travelling along +x direction.
- A wave travelling along -x direction
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
- $x = 2 sin (2 \pi t-3 x)$
- $x = 2 sin (2 \pi t+3 x)$
- $x = 2 sin (2 \pi t-3 x+ \pi)$
- $x = 2 sin (2 \pi t-3 x+\pi/3)$
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
- $\pi $ rads
- $\pi/2 $ rads
- $\pi/3 $ rads
- none of the above
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
- A
- A/2
- 2A
- 3A/2
A traveling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and
- The wavelength is 5 m
- The frequency is 5 Hz
- The velocity of propagation is 5 m/s
- The wavelength is 0.2 m
A string is vibrating in $n$ loops. The number of nodes and antinodes respectively are
- $n, n$
- $(n+1), n$
- $n, (n-1)$
- $(n-1), n$
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).
- $S=A\cos\left(\dfrac{5\pi}{4}x\right)\sin\left(400\pi t\right)$
- $S=A\cos\left(\dfrac{5\pi}{8}x\right)\cos\left(1000\pi t\right)$
- $P _{ex}=A\cos\left(\dfrac{5\pi}{8}x\right)\sin\left(200\pi t\right)$
- $P _{ex}=A\sin\left(\dfrac{25\pi}{8}x\right)\cos\left(1000\pi t\right)$
The equation of a traveling and stationary wave are ${ y } _{ 1 }=a sin(\omega t-kx)$ and ${ y } _{ 2 }=a \sin kx \cos \omega t$. The phase difference between two point ${ x } _{ 1 }=\dfrac { \pi }{ 4k }$ and $ { x } _{ 2 }=\dfrac { 4\pi }{ 3k } $ are ${ \phi } _{ 1 }$ and ${ \phi } _{ 2 }$ respectively for two waves where k is the wave number, the ratio of ${ \phi } _{ 1 }/{ \phi } _{ 2 }$
- 6/7
- 16/3
- 12/13
- 13/12
A standing wave pattern is formed on a string. One of the waves is given by equation $Y _ { 1 } a \cos ( \omega t - K X + \pi / 3 )$ then the equation of the other wave such at $X = 0$ a noode is formal
- $y _{ 2 } = \operatorname { a sin } \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
- $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { \pi } { 3 } \right)$
- $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 2 \pi } { 3 } \right)$
- $y _ { 2 } = a \cos \left( \omega t + K X + \dfrac { 4 \pi } { 3 } \right)$
Two simple harmonic waves of amplitude 5 cm and 3 cm and of the same frequency travelling with the same speed in opposite directions superpose to produce stationary waves. The ration of the amplitude at a node to that at an antinode in the resultant wave is
- zero
- infinity
- 5:3
- 1:4
The equation of stationary wave is given by $y=5, cos (\pi x/3), sin 40 \pi t$ where y and x are given in cm and time t in second. Then a node occurs at the following distance
- 3 cm
- 10 cm
- 5 cm
- 1.5 cm
A $string$ is stretched between fixed points separated by $75.0\ cm$. It is observed to have resonant frequencies of $420\ Hz$ and $315\ Hz$. There are no other resonant frequencies between these two.
Then, the lowest resonant frequency for this string is :
- $1.05$Hz
- $1050$Hz
- $10.5$Hz
- $105$Hz
A wave represented by $y=2 cos (4x-\pi t)$ is superposed with another wave to form a stationary wave such that the point x= 0 is a node. The equation of other wave is:
- $2 sin(4x+\pi t)$
- $-2 cos (4x -\pi t)$
- $-2 cos (4x +\pi t)$
- $-2 sin (4x -\pi t)$