Halliday, Resnick & Walker — Waves–I: Problem Problem_87

A wave on a string is described by \( y(x, t) = 15.0 \sin(\pi x/8 - 4\pi t) \), where \( x \) and \( y \) are in centimeters and \( t \) is in seconds. (a) What is the transverse speed for a point on the string at \( x = 6.00 \text{ cm} \) when \( t = 0.250 \text{ s} \)? (b) What is the maximum transverse speed of any point on the string? (c) What is the magnitude of the transverse acceleration for a point on the string at \( x = 6.00 \text{ cm} \) when \( t = 0.250 \text{ s} \)? (d) What is the magnitude of the maximum transverse acceleration for any point on the string?