Waves Test - 77...

Wave in a medium is represented by the equation $$ y=0.2 sin [ \pi (x-4t) ] $$ meter. the displacement at a point x=50 cm and t=0.25 s is

Two particles executing SHM of same frequency, meet at x=+A/2, while moving in opposite directions. Phase difference between the particles is 

A mass M, attached to a horizontal spring,executes S.H.M. with amplitude $$A_1$$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude $$A_2$$. The ratio of $$(\frac{A_1}{A_2}$$ is :-

If tangent and normal to the curve $$y=2\sin{x}+\sin{2x}$$ are drawn at $$P\left(x=\cfrac{\pi}{3}\right)$$ then area of the quadrilateral formed by tangent, the normal at $$P$$ and the coordinate axes is 

Two waves have equations $${x}_{1}=a\sin{(\omega t+{\phi}_{1})}$$ and $${x}_{2}=a\sin{(\omega t+{\phi}_{2})}$$. If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves. The phase difference between them is:

A particle performs simple harmonic motion with amplitude $$A$$. Its speed is trebled at the instant that it is at a distance $$\dfrac { 2A }{ 3 }$$ from equilibrium position. The new amplitude of the motion is:

A $$1000$$ m long rod of density $$10.0 \times 10^4\, kg/m^3$$ and having Young's modulus $$Y=10^{11} \, Pa$$, is clamped at one end. It is hammered at the other free end as shown in the figure. The longitudinal pulse goes to the right end, gets reflected and again returns to the left end. How much time (in sec) the pulse will take to go to initial point?

Two uniform strings $$A$$ and $$B$$ made of steel are made to vibrate under the same tension. If the first overtone of $$A$$ is equal to the second overtone of $$B$$ and if the radius of $$A$$ is twice that of $$B$$, the ratio of the length of the strings is

A particle is executing SHM with amplitude $$A$$ has maximum velocity $${v}_{0}$$. Its speed at displacement $$\cfrac{3A}{4}$$ will be

One end of a spring of force constant K is attached to the ceiling of a lift. A body of mass m is attached to another end of the spring. If the cable of the lift suddenly breaks, then the amplitude of oscillation of the body in the freely falling lift will be :