CALC A thin, taut string tied at both ends and oscillating in its third harmonic has its shape described by the equation y(x, t) = (5.60 cm) sin [(0.0340 rad/cm)x] sin[(50.0 rad/s)t], where the origin is at the left end of the string, the x -axis is along the string, and the y -axis is perpendicular to the string. (a) Draw a sketch that shows the standing-wave pattern. (b) Find the amplitude of the two traveling waves that make up this standing wave. (c) What is the length of the string? (d) Find the wavelength, frequency, period, and speed of the traveling waves. (e) Find the maximum transverse speed of a point on the string. (f) What would be the equation y(x, t) for this string if it were vibrating in its eighth harmonic?
Solution 43E Step 1of 8: Introduction: Since the string is tied at both the ends, the wave is a non traveling one i.e. it is a standing wave. The third harmonic equation is given by, y(x, t) = (5.60 cm) sin [(0.0340 rad/cm)x] sin[(50.0 rad/s)t]