A taut string of length 1.50m is fixed at both ends. A sinusoidal pulse generator at the left end (x=0) sends a continuous travelling wave described by
yinc(x,t)=4.0mmsin(4πx−120πt),
where x is in metres, t in seconds, and the numerical arguments of the sine function are in radians. The right end at x=1.50m is rigidly fixed, so the wave reflects there with an appropriate phase change.
(a) Write an explicit expression for the reflected wave yref(x,t) that travels toward the left. Specify any phase reversal required by the fixed boundary condition.
(b) Obtain the expression for the resultant standing wave on the string by adding yinc and yref. Present your result in a form that clearly displays the spatial and temporal factors separately.
(c) From your standing‐wave expression, determine the distance between adjacent nodes on the string.
(d) Identify which harmonic of the string is being excited by the pulse generator and justify your answer with reference to the standing‐wave pattern and the string length.