Question

A wave traveling in a string in the positive x direction has a wavelength of 35 cm, an amplitude of 8.4 cm, and a period of 1.2 s. What is the wave equation (in base SI units) that correctly describes this wave?

y(x,t)=0.084 sin(18x+5.2t)

y(x,t)=0.084 sin(18x−5.2t)

y(x,t)=0.084 sin(0.35x+1.2t)

y(x,t)=0.084 sin(0.35x−1.2t)

y(x,t)=0.084 sin(2.9x−0.83t)

Answer 1

For a wave travelling in the positive x-direction, the wave equation can be written as,

y = Asin(kx - wt)

where
A is the amplitude
k is the wave number
w is the angular frequency

Amplitude is given as 8.4 cm = 0.084 m
A = 0.084 m (S.I. Unit)

wave number k is

k = 2*3.14/(0.35 m) = 17.94 m^-1 = (S.I. Unit)

and an angular frequency is
T is time period
w = 5.23 s^-1 = (S.I. Unit)

Now the equation can be written as,
y(x,t)=0.084 sin(18x−5.2t)