The equation of displacement of two waves are given as y1=10 sin(3 πt+(π)/(3)) ; y2=5 [sin3 πt

Name: Problem 20, Chapter 12: Genius Physics (Class 11) - For IIT-JEE and CBSE
Uploaded: 2022-02-25T16:52:35-08:00
Duration: 1 min 37 s
Channel: Rubeena Zulfiqar
Description: The equation of displacement of two waves are given as y1=10 sin(3 πt+(π)/(3)) ; y2=5 [sin3 πt+√(3) cos3 π] Then what is the ratio of their amplitudes (a) 1: 2 (b) 2: 1 (c) 1: 1 (d) None of these

step 1 Given in this question is, as the equation of displacement of two waves are given, the equation

Question

The equation of displacement of two waves are given as $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) ; \quad y_{2}=5$ $[\sin 3 \pi t+\sqrt{3} \cos 3 \pi]$ Then what is the ratio of their amplitudes (a) $1: 2$ (b) $2: 1$ (c) $1: 1$ (d) None of these

   The equation of displacement of two waves are given as $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) ; \quad y_{2}=5$ $[\sin 3 \pi t+\sqrt{3} \cos 3 \pi]$
Then what is the ratio of their amplitudes
(a) $1: 2$
(b) $2: 1$
(c) $1: 1$
(d) None of these

Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal 1st Edition

Chapter 12, Problem 20

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Solved by Expert Rubeena Zulfiqar

02/25/2022

Step 1

Step 1: The given equations of displacement of two waves are $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right)$ and $y_{2}=5 [\sin 3 \pi t+\sqrt{3} \cos 3 \pi]$. Show more…

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The equation of displacement of two waves are given as $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) ; \quad y_{2}=5$ $[\sin 3 \pi t+\sqrt{3} \cos 3 \pi]$ Then what is the ratio of their amplitudes (a) $1: 2$ (b) $2: 1$ (c) $1: 1$ (d) None of these

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Key Concepts

Phasor Representation

Phasor representation is a technique used to simplify the analysis of sinusoidal functions by treating the sine and cosine terms as orthogonal components in a complex plane. This method helps in visualizing and calculating the resultant amplitude and phase shift when multiple sinusoidal functions are combined.

Combination of Sine and Cosine Terms

When a sinusoidal function is represented as a combination of sine and cosine functions with the same angular frequency, the overall amplitude can be determined using the Pythagorean theorem. Specifically, if the function is written as A sin(?t) + B cos(?t), the equivalent single wave has an amplitude of ?(A² + B²), which captures the combined effect of both components.

Amplitude

Amplitude is the maximum displacement of a wave from its equilibrium position. In sinusoidal functions, it represents the peak value of the oscillations and is a key characteristic of the wave’s energy and intensity.

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