How can I evaluate an equation within a String?

A transverse wave on a string is described by the equation y(x, t) = (2.31 cm) sin[(110 rad/s)t + (10 rad/s)x]?

• What is the maximum transverse speed of a point on the string? What is the maximum transverse acceleration of a point on the string? How fast does the wave move along the string? Why is your answer to (c) different from the answer to (a)?

• Answer:

  maximum transverse speed of a point on the string(particle velocity) = 254.1cm/s maximum transverse acceleration of a point on the string = 27951 sqcm/s the wave moves along the string at a speed of 11 cm/s (speed of wave). Particle velocity should not be confused with the speed of the wave as it passes through the medium, i.e. in the case of a sound wave, particle velocity is not the same as the speed of sound. The wave moves relatively fast, while the particles oscillate around their original position with a relatively small particle velocity.