sinusoidal wave travels along a string, The time fora particular point to move from maximum displacement to zero is 0.28 s. What re the (a) period and (b) frequency? (c) The wavelength is 1.4 m ; what is the wave specd?

We start by noting that the motion of a point on the string is simple harmonic. In such motion, the displacement can be described by a cosine function. For a cosine function, moving from the maximum (cosine of zero phase, which is 1) to the equilibrium position (where the cosine is 0) takes one-quarter of a full cycle. (a) The time for a quarter period is given as 0.28 s. Therefore, the full period T is   T = 4 × 0.28 s = 1.12 s. (b) Frequency f is the reciprocal of the period:   f = 1/T = 1/1.12 s ≈ 0.89 Hz. (c) The wave speed v is related to the wavelength λ and the period T by   v = wavelength / period = 1.4 m / 1.12 s ≈ 1.25 m/s. Thus, the answers are:  (a) Period T = 1.12 s,  (b) Frequency f ≈ 0.89 Hz,  (c) Wave speed v ≈ 1.25 m/s.