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Waves Problems




In this page we have Waves Problems for JEE Main/Advanced . Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1.
If a wave form has the equation
$y_1=P \sin( \omega t-kx)$
$y_2=Q \cos(\omega t-kx)$
Find
(a) The resulting equation on superimposition
(b) Find the amplitude of the superimposed wave

Question 2.
A standing wave results from the sum of two transverse travelling waves given by
$y_1=\cos( \pi x-4 \pi t)$
$y_2=\cos( \pi x + 4 \pi t)$
find
(a)Equation of wave
(b) What is the amplitude of oscillation at an anti-node?
(c) What is the smallest positive value of x that corresponds to a node
(d) At what time during the interval 0 <= t <=.50 sec,will the particle at x=0 have zero velocity

Question 3.
You are driving 8 m/s on a straight road and sounding a horn which you hear at a frequency of 600Hz. The sound of the horn gets reflected from the high rise building ahead and you hear the echo.
(a)What is the frequency of the echo you hear?
(b)What beat frequency you hear?

Question 4.

Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle. Assume that the sound of the whistle is composed of components varying in frequency from f1 = 800 Hz to f2 = 1120 Hz. The spread in the frequency (highest frequency - lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.
(i). The speed of sound of the whistle is
(a) 340 m/s for passengers in A and 310 m/s for passengers in B
(b) 360 m/s for passengers in A and 310 m/s for passengers in B
(c) 310 m/s for passengers in A and 360 m/s for passengers in B
(d) 340 m/s for passengers in both the trains

(ii). The spread of frequency as observed by the passengers in train B is
(a) 310 Hz
(b) 330 Hz
(c) 350 Hz
(d) 290 Hz

Question 5.
A car is being driven towards a cliff at 100km/h. The horn is sounded for a short time. The frequency of the horn is 440Hz.An echo from the cliff is heard by the driver of the car and also by a stationary observer. If the speed of sound is 340m/s, calculate the apparent frequency of the echo as perceived by
(a) the stationary observer
(b) the driver of the car.

Question 6.

In the given progressive wave $y = 5 \sin (100 \pi t – 0.4 \pi x )$
where y and x are in m, t is in s. What is the
(a) amplitude
(b) wave length
(c) frequency
(d) wave velocity
(e) particle velocity amplitude
Answer
(a) 5m
(b) 5m
(c) 50Hz
(d) 250m/s
(e) $500 \pi$ m/s

Question 7.
The displacement of an elastic wave is given by the function
$y = 12 \sin \omega t + 5 \cos \omega t$.
where y is in cm and t is in second. Calculate the resultant amplitude
Answer
13 cm

Question 8.
A whistle of frequency of 540 Hz is moving in a circle of radius 2 ft with angular velocity 15 rad/s. What is the lowest and highest frequencies heard by the listener standing at rest far away from the center of the circle . Velocity of sound in are is 1100 ft/sec
Answer
$f_{max} = 555 \ Hz$
$f_{min} = 525 \ Hz$

Question 9
Two waves are represented by the equations
$y_1=5 \sin( \omega t +kx+0.57)$m and
$y_2=5 \cos(\omega t+kx)$m
where x is in meter and t in sec. Find the phase difference between them
Answer
1 rad

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