Principle of Superposition

Author:D. C. Pandey
JEE Advanced
IMPORTANT

Important Questions on Principle of Superposition

HARD
IMPORTANT

Two pulses travelling in opposite directions along a string are shown for t=0 in the figure. Plot the shape of the string at t=1.0, 2.0, 3.0, 4.0 and 5.0 s, respectively.

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MEDIUM
IMPORTANT

Two sinusoidal waves combining in a medium are described by the equations
y1=(3.0 cm)sinπ(x+0.60 t)
and y2=(3.0 cm)sinπ(x-0.60 t)
where x is in cm and t is in s. Determine the maximum displacement of the medium at
(a) x=0.250 cm
(b) x=0.500 cm and
(c) x=1.50 cm
(d) Find the three smallest values of x corresponding to antinodes.

MEDIUM
IMPORTANT

A wave pulse on a string has the dimensions shown in figure. The wave speed is v=1 cm s-1.

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(a) If point O is a fixed end, draw the resultant wave on the string at t=3 s and t=4 s.
(b) Repeat part (a) for the case in which O is a free end.

EASY
IMPORTANT

Two transverse waves A and B superimpose to produce a node at x=0. If the equation of wave A is y=acos(kx+ωt), then the equation of wave B is

EASY
IMPORTANT

Two identical harmonic pulses traveling in opposite directions in a taut string approach each other. At the instant when they completely overlap, the total energy of the string will be

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MEDIUM
IMPORTANT

Sources separated by 20 m vibrate according to the equation y1=0.06 sin(πt) and y2=0.02 sin(πt). They send out waves along a rod with speed 3 m s-1. What is the equation of motion of a particle 12 m from the first source and 8 m from the second, y1, y2 are in m ?

HARD
IMPORTANT

Incident wave y=A sinax+bt+π2 is reflected by an obstacle at x=0 which reduces intensity of reflected wave by 36%. Due to superposition, the resulting wave consists of a standing wave and a travelling wave given by y=-1.6 sinax sinbt+cA cos(bt+ax) where A, a, b and c are positive constants.

Position of second antinode is

HARD
IMPORTANT

Incident wave y=A sinax+bt+π2 is reflected by an obstacle at x=0 which reduces intensity of reflected wave by 36%. Due to superposition, the resulting wave consists of a standing wave and a travelling wave given by y=-1.6 sinax sinbt+cA cos(bt+ax) where A, a, b and c are positive constants.

Value of c is

MEDIUM
IMPORTANT

Two waves y1=A sin(ωt-kx) and y2=A sin(ωt+kx) superimpose to produce a stationary wave, then

HARD
IMPORTANT

A man generates a symmetrical pulse in a string by moving his hand up and down. At t=0, the point in his hand moves downwards from the mean position. The pulse travels with speed 3 m s-1 on the string and his hand passes 6 times in each second from the mean position. Then, the point on the string at a distance 3 m will reach its upper extreme first time at t=

EASY
IMPORTANT

Three one-dimensional mechanical waves in an elastic medium is given as,
y1=3A sin(ωt-kx), y2=A sin(ωt-kx+π) and y3=2A sin(ωt+kx) are superimposed with each other. The maximum displacement (amplitude) of the medium particle would be