Chapter 2: Q49P (page 500)
A transverse sine wave with an amplitude of 2.50 mm and a wavelength of 1.80 m travels from left to right along a long, horizontal, stretched string with a speed of 36.0 m/s. Take the origin at the left end of the string has its maximum upward displacement.
(a) What are the frequency, angular frequency, and wave number of the wave?
(b) What is the function \(y\left( {x,t} \right)\) that describes the wave?
(c) What is \(y\left( t \right)\)for a particle at the left end of the string?
(d) What is \(y\left( t \right)\) for a particular 1.35 m to right of the origin?
(e) What is the maximum magnitude of transverse velocity of any particle of the string?
(f) Find the transverse displacement and the transverse velocity of a particle 1.35 m to the right of the origin at time \(t = 0.0625\;s\).
Short Answer
Thus, (a) the frequency is \(20\;{\rm{Hz}}\), angular frequency is \(40\pi \;{{\rm{s}}^{{\rm{ - 1}}}}\) and wave number is \(3.49\;{{\rm{m}}^{{\rm{ - 1}}}}\).