Explanation Write the equation for the sinusoidal wave shape. D = A sin ( k x − ω t ) Here, D is the displacement, A is the amplitude, k is the propagation constant and ω is the angular frequency. Differentiate the above equation partially with respect to time. ∂ D ∂ t = − A ω cos ( k x − ω t ) v ′ = − A ω cos ( k x − ω t ) Here, v ′ is the transverse speed of the wave. For the maximum value of v ′ , cos ( k x − ω t ) should be equal to 1 . Substitute v ′ max for v ′ and 1 for cos ( k x − ω t ) in the above equation. | v ′ max | = A ω ( 1 ) = A ω (I) Write the expression to obtain the wave velocity. v = f λ (II) Here, v is the wave velocity, f is the frequency of the wave and λ is the wavelength of the wave

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Author: GIANCOLI

Publisher: VST

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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 39P

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The assumption A<<λ implies that the maximum transverse speed v′max of the string itself is much less than the wave velocity and also the ratio of v′max/v.

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Chapter 15, Problem 38P

Chapter 15, Problem 40P

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Chapter 15 Solutions

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The assumption A < < λ implies that the maximum transverse speed v ′ max of the string itself is much less than the wave velocity and also the ratio of v ′ max / v .

Solution Summary: The author explains the assumption Alambda implies that the maximum transverse speed of the string is much less than the wave velocity.

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The assumption A<<λ implies that the maximum transverse speed v′max of the string itself is much less than the wave velocity and also the ratio of v′max/v.

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Chapter 15 Solutions

The assumption A &lt; &lt; λ implies that the maximum transverse speed v ′ max of the string itself is much less than the wave velocity and also the ratio of v ′ max / v .

Solution Summary: The author explains the assumption Alambda implies that the maximum transverse speed of the string is much less than the wave velocity.

Concept explainers

The assumption A<<λ implies that the maximum transverse speed v′max of the string itself is much less than the wave velocity and also the ratio of v′max/v.

Want to see the full answer?

Chapter 15 Solutions

The assumption A < < λ implies that the maximum transverse speed v ′ max of the string itself is much less than the wave velocity and also the ratio of v ′ max / v .