Question

A long string carries a wave; a 5.40-m segment of the string contains three complete wavelengths and has a mass of 180 g. The string vibrates sinusoidally with a frequency of 45.0 Hz and a peak-to-valley displacement of 19.0 cm.

how do you go about writing a formula in the form of A sin(kx+wt)??

Answer 1

Although you don't say so, the formula you are trying to fit indicates a traveling wave, not a standiung wave.

I don't see why you need the mass of the string. It does have a role in determining the wave speed, but so does the tension, which you do not provide.

Your wavelength is 5.4/3 = 1.8 m
Your angular frequency is
w = 2 pi f = 282.74 rad/s
Your amplitude is A = 9.5 cm

k = 2 pi/(wavelength) = 3.49 m^-1

Answer 2

the mass is important for part b. they must have just not included it. but it asks for the power in part b. you need the mass to find the inertial factor(mass/length)