Waves Test - 54...

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

A particle performing $$S.H.M$$ is found at its equilibrium at $$t= 1\ s$$ and it is found to have a speed of $$0.25\ m/s$$ at $$t=2\ s$$.If the period of oscillation is $$6\ s$$.Calculate amplitude of oscillation

The equation of a progressive wave are
$$Y=sin[200n(t-\cfrac x {330})]$$,where x is in meter and f is in second. The frequency and velocity of wave are

A $$4$$ kg particle is moving along the x-axis under the action of the force $$F=-\left(\dfrac{\pi^2}{16}\right)\times N$$. At $$t=2$$sec, the particle passes through the origin and at $$t=10$$ sec its speed is $$4\sqrt{2}$$m/s. The amplitude of the motion is?

Three waves of amplitude $$10\mu\ m,4\mu\ m$$ and $$7\mu\ m$$ arrive at a point with successive phase difference of $$\pi/2$$. The amplitude of the resultant wave is

An object of mass m is attached to a spring.The restoring force of the spring is F=$$ - \lambda {x^3},$$ where x is the displacement. the oscillation period  depends on the mass, $$\lambda $$ and oscillation amplitude.suppose the object is initially at rest.If the initial displacement is D then its period is $$\tau $$ .If the initial displacement is 2D, find the period.(Hint: Use dimension analysis.)

A transverse progressive wave on a stretched string has a velocity of $$10ms^{-1}$$ and frequency of $$100Hz$$. The phase difference between two particles of the string which nbare $$2.5cm$$ apart will be :

Equation of two $$S.H.M,\,\,{x_1} = 5\sin \left( {2\pi t + \pi /4} \right),\,{x_2} = 5$$ $$\sqrt 2 \left( {\sin 2\pi t + \cos 2\pi t} \right)$$. Ratio of amplitude & phase difference will be :

A wave is travelling along a string. At an instant shape of the string is as shown in figure. At this instant, point A is moving upwards. Which of the following statements is/are correct ?

In a string the speed of wave is $$10m/s$$ and its frequency is $$100$$ Hz. The value of the phase difference at a distance $$2.5$$cm will be :