The intensity ratio of two waves of same frequency and travelling in the same direction is 1:16. Calculate the ratio of their amplitudes.
To calculate the ratio of the amplitudes of two waves when the intensity ratio is given, you _______ ________ ___ ________ _________ _____.
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_____ ___ __________ ____ _______ ______.
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Establish the differential equation for simple harmonic motion (SHM) in one dimension. Show that for SHM, the velocity and acceleration of the particle is proportional to and
respectively, where
is the angular frequency of the particle.
What do you understand by wave impendence? Derive an expression for the impedance offered to sound waves propagating in a gaseous medium.
Standing waves are produced by the superposition of the following two waves:
y1 (x, t) = 0.2 sin (t - 2) and t2 (x,t) = 0.2 sin
(t+ 2x)
a) Obtain the resultant displacement of the particle at x at time t.
b) Calculate the value(s) of x for which displacement is zero.
c) Calculate the difference between two nearest values of x for which the displacement is zero. Is it related to the wavelength?
The natural angular frequency of an oscillator is 0. It is subjected to a damping force proportional to velocity and the damping force per unit mass per unit velocity is b. A periodic force given by F cos t is applied to it. Establish the differential equation for the oscillator and obtain the condition for velocity resonance.
The weight on a vertical spring undergoes forced vibrations according to the following equation:
where x is the displacement from the equilibrium position and > 0 is a constant. If at t = 0, x = 0 and
calculate x as a function of t.
The displacement of an object executing SHM is given by:
x = 0.02 cos 4 (t + 0.625)m
Calculate the amplitude, period, maximum velocity, maximum acceleration and initial displacement of the object.
i) Two collinear SHMs of amplitudes 3 and 4 units add up to an SHM of amplitude units. Calculate the phase difference between the two superposing SHMs.
ii) A particle is simultaneously subjected to two mutually perpendicular oscillations given by
x = 3 sin cm, y = 3 cos
cm Determine its trajectory of motion.