A wave is represented by the equation Y=7 sin(7 πt-0.04 πx+(π)/(3)) x is in meters and t is in

Name: Problem 9, Chapter 12: Genius Physics (Class 11) - For IIT-JEE and CBSE
Uploaded: 2022-02-25T14:28:58-08:00
Duration: 1 min 31 s
Channel: Rubeena Zulfiqar
Description: A wave is represented by the equation Y=7 sin(7 πt-0.04 πx+(π)/(3)) x is in meters and t is in seconds. The speed of the wave is (a) 175 m / sec (b) 49 πm / s (c) (49)/(π) m / s (d) 0.28 / s

step 1 The given data of the question is, as the wave is represented by equation, so a wave equation, t

Question

A wave is represented by the equation $Y=7 \sin \left(7 \pi t-0.04 \pi x+\frac{\pi}{3}\right) \quad x$ is in meters and $t$ is in seconds. The speed of the wave is (a) $175 \mathrm{~m} / \mathrm{sec}$ (b) $49 \pi \mathrm{m} / \mathrm{s}$ (c) $\frac{49}{\pi} \mathrm{m} / \mathrm{s}$ (d) $0.28 \mathrm{\pim} / \mathrm{s}$

   A wave is represented by the equation $Y=7 \sin \left(7 \pi t-0.04 \pi x+\frac{\pi}{3}\right) \quad x$ is in meters and $t$ is in seconds. The speed of the wave is
(a) $175 \mathrm{~m} / \mathrm{sec}$
(b) $49 \pi \mathrm{m} / \mathrm{s}$
(c) $\frac{49}{\pi} \mathrm{m} / \mathrm{s}$
(d) $0.28 \mathrm{\pim} / \mathrm{s}$

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

Pradeep Kshetrapal 1st Edition

Chapter 12, Problem 9

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Solved by Expert Rubeena Zulfiqar

02/25/2022

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04 \pi x+\frac{\pi}{3}\right)$ where $x$ is in meters and $t$ is in seconds. Show more…

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A wave is represented by the equation $Y=7 \sin \left(7 \pi t-0.04 \pi x+\frac{\pi}{3}\right) \quad x$ is in meters and $t$ is in seconds. The speed of the wave is (a) $175 \mathrm{~m} / \mathrm{sec}$ (b) $49 \pi \mathrm{m} / \mathrm{s}$ (c) $\frac{49}{\pi} \mathrm{m} / \mathrm{s}$ (d) $0.28 \mathrm{\pim} / \mathrm{s}$

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Key Concepts

Angular Frequency

Angular frequency, denoted by omega (?), represents how fast a periodic function oscillates in time and is measured in radians per second. It determines the temporal behavior of the wave and appears as the coefficient of the time variable in the wave equation.

Wave Number

The wave number, denoted by k, is measured in radians per unit length (e.g., per meter) and indicates the spatial frequency of the wave. It quantifies how many oscillations occur per unit distance, and appears as the coefficient of the spatial variable in the wave equation.

Wave Speed

Wave speed, or phase velocity, is the rate at which a point of constant phase on the wave travels through space. It is calculated by the ratio of the angular frequency to the wave number (v = ?/k), linking the temporal and spatial characteristics of the wave.

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