Question

The dispalcement of a particle executing periodic motion is given by $y=4{\cos }^2\left(\frac{t}{2}\right)\sin 1000\omega t.$
This expression may be considered to be a result of superposition of :

• A. Two waves
• B. Three waves
• C. Four waves
• D. Five waves

Answer 1

The correct option is B Three waves

$y=4{\cos }^2\left(t/2\right)\sin \left(10\omega t\right)$

$=2\left[2{\cos }^2\right(t/2\left)\sin \right(10\omega t\left)\right]$

$=2\left[\right(1+\cos t\left)\sin \right(10\omega t\left)\right]$

$=2\sin \left(10\omega t\right)+2\sin \left(10\omega t\right)\cos t$

$=2\sin \left(10\omega t\right)+\sin \left(10\omega t\right)+\sin \left(999t\right)$