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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Could you please help me out solving question 9? I don't really understand how to do it
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F267b756b-4631-45c0-98bc-62ca391f0187%2F39926457-3b36-4499-9a8f-57c12a37f1b3%2F78tzrsg_processed.jpeg&w=3840&q=75)
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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