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1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).

1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).

Advanced Engineering Mathematics
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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1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).
Transcribed Image Text:1) If you pluck a guitar string, pulling it to a height of A and letting go, we can model its motion as f(t) = A cos(t), where t is in milliseconds and A is a constant. a. The derivative tells you how fast the string is moving, and thus how loud the sound will be. Find the derivative. b. The faster it moves (bigger derivative), the louder it will be. What is the relationship between how far you pluck the string, A, and how loud it is? c. What is wrong with our model as t gets big (as compared to what you expect from a real guitar string).
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