Question

The displacement $y$ of a particle in a medium can be expressed as, $y=10^{-6} \sin \left(100 t+20 x+\frac{\pi}{4}\right) m$ where $\mathrm{t}$ is in second and $x$ in meter. The speed of the wave is $[2004]$ (A) $20 \mathrm{~m} / \mathrm{s}$ (B) $5 \mathrm{~m} / \mathrm{s}$ (C) $2000 \mathrm{~m} / \mathrm{s}$ (D) $5 \pi \mathrm{m} / \mathrm{s}$

Name: Problem 290, Chapter 9: A Complete Resource Book in Physics for JEE MAIN
Uploaded: 2021-10-11T15:48:59-08:00
Duration: 1 min 17 s
Channel: Dheeraj Sharma
Description: The displacement y of a particle in a medium can be expressed as, y=10^-6 sin(100 t+20 x+(π)/(4)) m where t is in second and x in meter. The speed of the wave is [2004] (A) 20 m / s (B) 5 m / s (C) 2000 m / s (D) 5 πm / s

   The displacement $y$ of a particle in a medium can be expressed as, $y=10^{-6} \sin \left(100 t+20 x+\frac{\pi}{4}\right) m$ where
$\mathrm{t}$ is in second and $x$ in meter. The speed of the wave is $[2004]$
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $5 \mathrm{~m} / \mathrm{s}$
(C) $2000 \mathrm{~m} / \mathrm{s}$
(D) $5 \pi \mathrm{m} / \mathrm{s}$

A Complete Resource Book in Physics for JEE MAIN

Sanjeev Kumar 1st Edition

Chapter 9, Problem 290

Instant Answer

Solved by Expert Dheeraj Sharma

10/11/2021

Step 1

Comparing the given equation with the general wave equation, we have: $A = 10^{-6} m$ $k = 20$ $\omega = 100$ $\phi = \frac{\pi}{4}$ Show more…

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The displacement $y$ of a particle in a medium can be expressed as, $y=10^{-6} \sin \left(100 t+20 x+\frac{\pi}{4}\right) m$ where $\mathrm{t}$ is in second and $x$ in meter. The speed of the wave is $[2004]$ (A) $20 \mathrm{~m} / \mathrm{s}$ (B) $5 \mathrm{~m} / \mathrm{s}$ (C) $2000 \mathrm{~m} / \mathrm{s}$ (D) $5 \pi \mathrm{m} / \mathrm{s}$

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Key Concepts

Wave Equation

A wave equation describes the displacement of a point in a medium as a sinusoidal function of time and space. It typically includes terms for amplitude, angular frequency, spatial frequency (wave number), and phase constant.

Angular Frequency

Angular frequency is the rate at which the wave oscillates in time, measured in radians per unit time. In the wave equation, it is the coefficient of the time variable, and it determines how quickly the wave cycles repeat over time.

Wave Number

The wave number represents the spatial frequency of the wave, measured in radians per unit distance. It is the coefficient of the spatial variable in the wave equation and indicates the number of wave cycles per unit length.

Wave Speed

Wave speed is the rate at which the wave propagates through the medium. It is calculated as the ratio of angular frequency to the wave number (v = ?/k), linking the time-dependent oscillations with the spatial periodicity of the wave.

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