AP EAMCET · PHYSICS · Waves and Sound

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

A $\frac{a+b}{a b}$
B $\frac{\sqrt{a}+\sqrt{b}}{a b}$
C $\frac{\sqrt{a} \pm \sqrt{b}}{a b}$
D $\sqrt{\frac{a+b}{a b}}$

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Answer & Solution

Correct Answer

(D) $\sqrt{\frac{a+b}{a b}}$

Step-by-step Solution

Detailed explanation

The displacement equation presented by $\begin{aligned} & y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t \\ & =\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \sin \left(\omega t+\frac{\pi}{2}\right)\end{aligned}$ Here phase difference…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following:

	Column $- I$		Column $- II$
(a)	Transverse wave through a steel rod	(i)	$\sqrt{B + (\frac{4}{3}) \frac{η}{ρ}}$
(b)	Longitudinal waves in earth's crust	(ii)	$\sqrt{\frac{η}{ρ}}$
(c)	Longitudinal waves through a steel rod	(iii)	$\sqrt{\frac{2 π T}{g λ}}$
(d)	Ripples	(iv)	$\sqrt{\frac{λ}{ρ}}$

AP EAMCET 2021 Hard

A body of mass $2 \mathrm{~kg}$ moving in $\mathrm{X}-\mathrm{Y}$ plane has a potential energy given by $\mathrm{U}=(6 x+8 y) \mathrm{J}$. The body is at rest at the point $(3,2) \mathrm{m}$. The work to be done by the body to reach another position after $2 \mathrm{~s}$ is

AP EAMCET 2018 Medium

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

Answer & Solution

Step-by-step Solution

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

Step-by-step Solution

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