SATHEE: Wave Motion 5 Question 7

Wave Motion 5 Question 7

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

$y = 4 \cos^{2} (\frac{1}{2} t) \sin (1000 t)$

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

$(1992, 2 M)$

(a) two

(b) three

(d) five

Show Answer

Answer:

Correct Answer: 7. (b)

Solution:

The given equation can be written as

$\begin{aligned} y & = 2 (2 \cos^{2} \frac{t}{2}) \sin (1000 t) \\ y & = 2 (\cos t + 1) \sin (1000 t) \\ = 2 \cos t \sin 1000 t + 2 \sin (1000 t) \\ = \sin (1001 t) + \sin (999 t) + 2 \sin (1000 t) \end{aligned}$

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

Wave Motion 5 Question 7

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Wave Motion 5 Question 7

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

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