Question

A transverse harmonic wave on a string is described by y(x, t)=3.0 sin (36 t +0.018 x + π/4) where x and y are in cm and tin s. The positive direction of x is from left to right: What is the initial phase at the origin?

Answer 1

standard equation of traveling wave is
$y(x,t)=asin(\omega t+kx+\theta)$...(1)

where a is the amplitude, $\omega$ is the angular frequency , k is wave number. e.g., k = 2π/wavelength. and $\theta$ phase constant.

given, A transverse harmonic wave on a string is described by y(x, t)=3.0 sin (36 t +0.018 x + π/4).....(2)

compare both equations (1) and (2),
then, you will get, intimal phase at the origin, $\theta$ is π/4.