Waves Test - 42...

The path difference between two waves
$$y_{1} = a_{1}\sin \left (\omega t - \dfrac {2\pi x}{\lambda}\right )$$ and
$$y_{2} = a_{2}\cos \left (\omega t - \dfrac {2\pi x}{\lambda} +\phi \right )$$ is

Equations of a stationary and a travelling waves are as follows, $${ y }_{ 1 }=a\sin { kx } \cos { \omega t } $$ and $${ y }_{ 2 }=a\sin { \left( \omega t-kx \right)  }$$. The phase difference between two points $${ x }_{ 1 }=\dfrac { \pi  }{ 3k } $$ and $${ x }_{ 2 }=\dfrac { 3\pi  }{ 2k } $$ are $${ \phi  }_{ 1 }$$ and $${ \phi  }_{ 2 }$$ respectively for two waves. The ratio $$\dfrac { { \phi  }_{ 1 } }{ { \phi  }_{ 2 } } $$ is :

The minimum phase difference between two simple harmonic oscillations,
$$y_1  = \dfrac{1}{2} sim \omega t + \dfrac{\sqrt 3}{2} cos \omega t$$
$$y_2 = sim \omega t + cos \omega t$$, is

Two particles move parallel to $$x$$-axis about the origin with same amplitude and frequency. At a certain instant they are found at a distance $$\dfrac{a}{3}$$ from the origin on opposite sides but their velocities are found to be in same direction.Then the phase difference between two particles will be  

The ratio of amplitudes of two simple harmonic motions represented by the equations $$y_1=5 \sin \begin{pmatrix}2\pi t + \dfrac{\pi}{4}\end{pmatrix}$$ and $$y_2=2\sqrt{2} (\sin 2\pi t + \cos 1\pi t)$$ is

If the equation $$y_{1} = A\sin \omega t$$ and $$y_{2} = \dfrac {A}{2}\sin \omega t + \dfrac {A}{2}\cos \omega t$$ represent SHM then the ratio of the amplitudes of the two motions is

The equation of simple harmonic wave is given by $$ y=6 \,sin \,2\pi ( 2 t-0.1 x),$$ where $$ x $$ and $$ y $$ are in mm and $$ t $$ is in seconds . The phase difference between two particles $$ 2 mm $$ apart at any instant is 

In a ripple tank when one pulse is sent every tenth of a second , the distance between consecutive pulses is $$30 mm$$. In the same depth of water pulses are produced at half second intervals. What is the new distance between consecutive pulses ?

Two particles P and Q describe SHM of same amplitude a frequency v along the same straight line. The maximum distance between two particles is $$\displaystyle \sqrt { 2a } $$. The initial phase difference between the particles is :

Five waveforms moving with equal speeds on the x-axis
$${ y }_{ 1 }=8\sin { \left( \omega t+kx \right)  } ;{ y }_{ 2 }=6\sin { \left( \omega t+\cfrac { \pi  }{ 2 } +kx \right)  } ;{ y }_{ 3 }=4\sin { \left( \omega t+\pi +kx \right)  } ;$$