Question

The displacement of an elastic wave is given by the function $y=3sin\omega t+4cos\omega t$, where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is

• A. $3cm$
• B. $4cm$
• C. $5cm$
• D. $7cm$

Answer 1

The correct option is C $5cm$

Here, we have given: $y=3sin\omega t+4cos\omega t$

So, two components are there, $3sin\omega t$ and $4cos\omega t$

where, individual amplitudes are given by

$A_1=3cms$ and $A_2=4cms.$

so , resultant amplitude will be,

$A=\sqrt{A_1^2+A_2^2}=\sqrt{3^2+4^2}$

$A=5cms$