Wave Motion 5 Question 7

7. The displacement y of a particle executing periodic motion is given by

y=4cos2(12t)sin(1000t)

This expression may be considered to be a result of the superposition of independent harmonic motions.

(1992,2M)

(a) two

(b) three

(c) four

(d) five

Passage Based Questions

Passage 1

Two trains A and B are moving with speeds 20m/s and 30m/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=800Hz to f2=1120Hz, as shown in the figure. The spread in the frequency (highest frequency-lowest frequency) is thus 320Hz. The speed of sound in air is 340m/s.

Show Answer

Solution:

  1. The given equation can be written as

y=2(2cos2t2)sin(1000t)y=2(cost+1)sin(1000t)=2costsin1000t+2sin(1000t)=sin(1001t)+sin(999t)+2sin(1000t)

i.e. the given expression is a result of superposition of three independent harmonic motions of angular frequencies 999, 1000 and 1001rad/s.



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक