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10. A string (of tension T and density p) with fixed ends at x = 0 and x = I is hit by a hammer so that u(x, 0) = o, and əu/Ət (x, 0) = V in [−8 + ½ 1,8 + 1/31] and Ju/Ət (x, 0) = 0 elsewhere. Find the solution explicitly in series form. Find the energy 2 2 Әһ Əh En(h) = +T dx 2 Ət მუ of the nth harmonic h = hn. Conclude that if 8 is small (a concentrated blow), each of the first few overtones has almost as much energy as the fundamental. We could say that the tone is saturated with overtones.

10. A string (of tension T and density p) with fixed ends at x = 0 and x = I is hit by a hammer so that u(x, 0) = o, and əu/Ət (x, 0) = V in [−8 + ½ 1,8 + 1/31] and Ju/Ət (x, 0) = 0 elsewhere. Find the solution explicitly in series form. Find the energy 2 2 Әһ Əh En(h) = +T dx 2 Ət მუ of the nth harmonic h = hn. Conclude that if 8 is small (a concentrated blow), each of the first few overtones has almost as much energy as the fundamental. We could say that the tone is saturated with overtones.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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10. A string (of tension T and density p) with fixed ends at x = 0 and x = I is hit by a hammer so that u(x, 0) = o, and əu/Ət (x, 0) = V in [−8 + ½ 1,8 + 1/31] and Ju/Ət (x, 0) = 0 elsewhere. Find the solution explicitly in series form. Find the energy 2 2 Әһ Əh En(h) = +T dx 2 Ət მუ of the nth harmonic h = hn. Conclude that if 8 is small (a concentrated blow), each of the first few overtones has almost as much energy as the fundamental. We could say that the tone is saturated with overtones.
Transcribed Image Text:10. A string (of tension T and density p) with fixed ends at x = 0 and x = I is hit by a hammer so that u(x, 0) = o, and əu/Ət (x, 0) = V in [−8 + ½ 1,8 + 1/31] and Ju/Ət (x, 0) = 0 elsewhere. Find the solution explicitly in series form. Find the energy 2 2 Әһ Əh En(h) = +T dx 2 Ət მუ of the nth harmonic h = hn. Conclude that if 8 is small (a concentrated blow), each of the first few overtones has almost as much energy as the fundamental. We could say that the tone is saturated with overtones.
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