A stretched string of length 1.20m is fixed at both ends and supports transverse waves that travel along the string with speed 160ms−1. Two sinusoidal waves of equal amplitude and identical frequency travel in opposite directions on the string, giving rise to a stable standing-wave pattern.
(a) Show that nodes of the standing wave occur at positions where the phase difference between the two traveling waves is an odd multiple of π.
(b) The string is vibrating in its second harmonic (first overtone). Calculate the wavelength and frequency associated with this mode.
(c) For the oscillation described in part (b), compute the phase difference between the two traveling waves at the point located 0.20m from the left end of the string and verify that this point is neither a node nor an antinode.
(d) Suppose the phase of one of the traveling waves is suddenly advanced by 2π while the other wave is unchanged. Predict, with explanation, the immediate effect of this change on the amplitude at the point 0.20m from the left end.