Waves Test - 57...

Two simple harmonic motions are represented by equations
$$ y _ { 1 } = 10 \sin ( 3 \pi t + \pi / 4 )$$ and
$$y _ { 2 } = 5 ( \sin 3 \pi t + \sqrt { 3 } \cos 3 \pi t ) \times 2 $$
Their amplitudes are in the ratio of 

The equation of a stationary wave is $$y=0.8cos\left( \dfrac { \pi x }{ 20 }  \right) \sin 200\pi t$$ where x is in cm and t is in seconds. The separation between consecutive nodes is

The displacement of a particle is given by x = 3 sin $$\left( 5\pi t \right) $$+ 4 cos$$\left( 5\pi t \right) $$ The amplitude of particle is 

The displacement of an oscillating particle varies with time (in seconds) according to the equations $$y(cm)=sin\dfrac { \pi  }{  2} (\dfrac { t  }{  2}+\dfrac { 1  }{  3} )$$. The maximum acceleration of the particle is approximately.

A tunnel is dug n the earth across one of its diameter. Two masses 'm' & '2m' are dropped from the ends of the tunnel. The masses collide and stick to each other and performs S.H.M. Then amplitude of S.H.M. will be : [R=radius of the earth]

Equation of motion in the same direction is given by $$y_1 = A \ sin(\omega t - kx),  y_2 = A \ sin(\omega t - kx - \theta)$$. The amplitude of the medium particle will be

A body executing simple harmonic motion has a maximum acceleration equal to $$24metre/sec^2$$ and maximum velocity equal to $$16meter/sec$$. The amplitude of simple harmonic motion is:

The amplitude of a particle executing $$SHM$$ is $$4cm$$. At the mean position the speed of the particle is $$16cm/sec$$. The distance of the particle from the mean position at which the speed of the particle becomes $$8\sqrt {  3} cm/s$$, will be:

A travelling wave $$Y = A$$ sin $$( k x - \omega t + \theta )$$ passes from a heavier string to lighter string. The reflected has amplitude $$0.5$$ $$A$$. The junction of the string is $$x = 0$$. The equation of the reflected wave is:

The amplitude of simple harmonic motion represented by the displacement equation  y(cm) = 4(sin 5$$\pi$$t + $$\sqrt2$$cos 5$$\pi$$t) is  :