Explanation Given Info : Longitudinal sound wave are produced in a long metal rod Formula to find the speed of the longitudinal wave produced in the rod is, v long = Y ρ v long is the speed of the longitudinal sound wave. Y is the young’s modulus for the material. ρ is the density of the material. Use m / V for ρ and π r 2 L for V in above relation. v long = Y V m = Y ( π r 2 L ) m (1) r is the radius of the rod. L is the length of the rod. m is the mass of the rod. Formula to find the speed of the transverse wave produced in the rod is, v trans = F μ v trans is the speed of the transverse sound wave. F is the tension force. μ is the linear density of the material. Use m / L for μ in above relation. v trans = F L m (2) The ratio of the speed of longitudinal wave and transverse wave is, v long v trans = 8 Rewrite the relation to find the tension force. v long = 8 v trans Compare the equation (1) and (2)

11th Edition

ISBN: 9781305965317

Author: SERWAY

Publisher: CENGAGE L

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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 14, Problem 81AP

To determine

The required tension in the rod.

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Chapter 14, Problem 80AP

Chapter 14, Problem 82AP

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