Question

A sinusoidal wave is traveling on a string with speed 30.00 cm/s. The displacement of the particles of the string at x = 15 cm is found to vary with time according to the equation y = (5.0 cm) sin[1.5 - (3.0 s-1)t]. The linear density of the string is 5.0 g/cm.

(a) What is the frequency of the wave?

(b) What is the wavelength of the wave?

(c) Give the general equation giving the transverse displacement of the particles of the string as a function of position and time.

(d) Calculate the tension in the string.

Answer 1

Unless you have a typo, sin[1.5 - (3.0 s-1)t] is really sin[1.5 - 2t]

when is 2 t equal to 2 pi ?? (that is when the argument of the sin function changes by 2 pi, a period)
That is when t increases by pi
so the period, T is pi
the frequency = 1/pi
wavelength is how far it goes in pi seconds
That is 30 * pi

y = (5.0 cm) sin[1.5 - 2t] sin (2 pi x/L - phi)
where L is that wavelength

get the phase angle phi from the value of y when x = 15 and t = 0

you have the speed of the wave c = L/T

You know the equation for speed of the wave versus tension and density, so calculate the tension.