The amplitude of a wave represented by the di | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given equation is of the form $y = A_1 \sin \omega t + A_2 \cos \omega t$,where $A_1 = \frac{1}{\sqrt{a}}$ and $A_2 = \frac{1}{\sqrt{b}}$.For

Vedclass · Accepted Answer

$\frac{\sqrt{a + b}}{\sqrt{ab}}$

Vedclass · Answer

(A) The given equation is of the form $y = A_1 \sin \omega t + A_2 \cos \omega t$,where $A_1 = \frac{1}{\sqrt{a}}$ and $A_2 = \frac{1}{\sqrt{b}}$.For an equation of the form $y = A_1 \sin \omega t + A_2 \cos \omega t$,the resultant amplitude $A$ is given by $A = \sqrt{A_1^2 + A_2^2}$.Substituting the values of $A_1$ and $A_2$:$A = \sqrt{\left(\frac{1}{\sqrt{a}}\right)^2 + \left(\frac{1}{\sqrt{b}}\right)^2}$$A = \sqrt{\frac{1}{a} + \frac{1}{b}}$$A = \sqrt{\frac{b + a}{ab}}$$A = \frac{\sqrt{a + b}}{\sqrt{ab}}$

The amplitude of a wave represented by the displacement equation $y = \frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$ will be

Similar Questions

The particles of a medium vibrate about their mean positions whenever a wave travels through that medium. The phase difference between the vibrations of two such particles

The equation of a progressive wave is given by $x = 0.05 \cos \left( 4\pi t + \frac{\pi}{4} \right) \, m$. What is the frequency of the wave in $Hz$?

The equation of a travelling wave is given by $y = 0.5 \sin(20x - 400t)$,where $x$ and $y$ are in meters and $t$ is in seconds. The velocity of the wave is .... $m/s$.

The wave described by $y = 0.25 \sin(10\pi x - 2\pi t)$,where $x$ and $y$ are in $meters$ and $t$ in $seconds$,is a wave travelling along:

$A$ transverse wave is given by $y = A \sin 2\pi \left( \frac{t}{T} - \frac{x}{\lambda} \right)$. The maximum particle velocity is equal to $4$ times the wave velocity when:

Vedclass Test Series

Exam Paper Generator

Online Exam Module