A wave travelling along the x -axis is described by the equation y(x, t)=0.005 Cos(∝x-βt) . If t

Name: Problem 1495, Chapter 10: JEE Physics
Uploaded: 2021-11-28T12:04:03-08:00
Duration: 1 min 17 s
Channel: Akshaya Rs
Description: A wave travelling along the x -axis is described by the equation y(x, t)=0.005 Cos(∝x-βt) . If the wavelength and the time period of the wave are 0.08 m and 2.0 s respectively, then ∝and βin appropriate units are ……(A) ∝=12.50 π, β=p / 2.0 (B) ∝=25 π, β=π(C) ∝=0.08 / π, β=2.0 / π(D) ∝=0.04 / π, a=1.0 / π

step 1 Hello everyone. In this question we will be understanding some basic concepts of the oscillation

Question

A wave travelling along the $\mathrm{x}$ -axis is described by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=0.005 \operatorname{Cos}(\propto \mathrm{x}-\beta \mathrm{t}) .$ If the wavelength and the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$ respectively, then $\propto$ and $\beta$ in appropriate units are $\ldots \ldots$ (A) $\propto=12.50 \pi, \beta=\mathrm{p} / 2.0$ (B) $\propto=25 \pi, \beta=\pi$ (C) $\propto=0.08 / \pi, \beta=2.0 / \pi$ (D) $\propto=0.04 / \pi, \mathrm{a}=1.0 / \pi$

   A wave travelling along the $\mathrm{x}$ -axis is described by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=0.005 \operatorname{Cos}(\propto \mathrm{x}-\beta \mathrm{t}) .$ If the wavelength and
the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$ respectively, then $\propto$ and $\beta$ in appropriate units are $\ldots \ldots$
(A) $\propto=12.50 \pi, \beta=\mathrm{p} / 2.0$
(B) $\propto=25 \pi, \beta=\pi$
(C) $\propto=0.08 / \pi, \beta=2.0 / \pi$
(D) $\propto=0.04 / \pi, \mathrm{a}=1.0 / \pi$

JEE Physics

StemEZ 1st Edition

Chapter 10, Problem 1495

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Solved by Expert Akshaya Rs

11/28/2021

Step 1

Step 1: The general equation of a wave is given by $y(x, t)=A \cos(kx-\omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. Show more…

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A wave travelling along the $\mathrm{x}$ -axis is described by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=0.005 \operatorname{Cos}(\propto \mathrm{x}-\beta \mathrm{t}) .$ If the wavelength and the time period of the wave are $0.08 \mathrm{~m}$ and $2.0 \mathrm{~s}$ respectively, then $\propto$ and $\beta$ in appropriate units are $\ldots \ldots$ (A) $\propto=12.50 \pi, \beta=\mathrm{p} / 2.0$ (B) $\propto=25 \pi, \beta=\pi$ (C) $\propto=0.08 / \pi, \beta=2.0 / \pi$ (D) $\propto=0.04 / \pi, \mathrm{a}=1.0 / \pi$

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Key Concepts

Wave Number

The wave number, often denoted by k, quantifies the spatial frequency of a wave. It is defined as k = 2?/?, where ? is the wavelength. This concept is central to describing how many oscillations occur per unit distance in a wave and appears in the spatial term of the wave equation.

Angular Frequency

Angular frequency, typically represented by ?, indicates how fast the wave oscillates in time and is given by ? = 2?/T, where T is the time period. It plays a key role in the temporal part of the wave equation by quantifying the number of radians per unit time.

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