Explanation The wave equation of the sinusoidal wave is, ∂ 2 D ∂ t 2 = ν 2 ∂ 2 D ∂ x 2 . Here, ν is the velocity of the wave. Write the expression of wavelength of the transverse wave. D ( x , t ) = e − ( k x − ω t ) 2 (I) Here, D is the displacement of the wave, A is the amplitude of the wave, k is the wave number, ω is the angular frequency and t is the time. Differentiate equation (I) with respect to x . ∂ D ∂ x = ( e − ( k x − ω t ) 2 ) [ − 2 ( k x − ω t ) ] ( k ) Again, differentiate the above equation with respect to x . ∂ 2 D ∂ x 2 = − 2 k [ ( e − ( k x − ω t ) 2 ) [ − 2 ( k x − ω t ) 2 ] ( k ) + k ( e − ( k x − ω t ) 2 ) ] ∂ 2 D ∂ x 2 = 2 k 2 e − ( k x − ω t ) 2 [ 2 ( k x − ω t ) 2 − 1 ] (II) Differentiate equation (I) with respect to t . ∂ D ∂ t = e − ( k x − ω t ) 2 [ − 2 ( k x − ω t ) ] ( − ω ) Again, differentiate the above equation with respect to t

Physics for Scientists & Engineers, Volume 2 (Chapters 21-35)

5th Edition

ISBN: 9780134378046

Author: GIANCOLI, Douglas

Publisher: PEARSON

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

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Chapter 15, Problem 38P

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Whether the equation D(x,t)=e−(kx−ωt)2 satisfies the wave equation.

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Chapter 15, Problem 37P

Chapter 15, Problem 39P

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Chapter 15 Solutions

Physics for Scientists & Engineers, Volume 2 (Chapters 21-35)

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Whether the equation D ( x , t ) = e − ( k x − ω t ) 2 satisfies the wave equation.

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Whether the equation D(x,t)=e−(kx−ωt)2 satisfies the wave equation.

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Chapter 15 Solutions