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A guitar string is fixed at both ends, as shown in the

A guitar string is fixed at both ends, as shown in the

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(6) A guitar string is fixed at both ends, as shown in the figure. When plucked, the string forms a standing wave y(z2₁t₁) of varying amplitude. The vertical displacement y of the string varies with position and time t and is given by y(x, t) = sin (#) sin(xt), x=0 y(1.1₂) for 0 ≤ ≤ 2 and t≥ 0. (a) Traces: (i) Show that, if we freeze time, the string will form a sine curve. (b) Give the period of the motion in time. 1 #1 *2 =2 (ii) Show that, if we focus on a single point on the string, we will see it oscillate up and down. X
Transcribed Image Text:(6) A guitar string is fixed at both ends, as shown in the figure. When plucked, the string forms a standing wave y(z2₁t₁) of varying amplitude. The vertical displacement y of the string varies with position and time t and is given by y(x, t) = sin (#) sin(xt), x=0 y(1.1₂) for 0 ≤ ≤ 2 and t≥ 0. (a) Traces: (i) Show that, if we freeze time, the string will form a sine curve. (b) Give the period of the motion in time. 1 #1 *2 =2 (ii) Show that, if we focus on a single point on the string, we will see it oscillate up and down. X
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