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? 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(0.35x+1.2t) y(x,t)=0.084 sin(2.9x−0.83t) y(x,t)=0.084 sin(18x+5.2t) y(x,t)=0.084 sin(0.35x−1.2t)

Answer 1

The correct answer is
y(x,t)=0.084 sin(18x-5.2t)
Let's see why. 

For a wave travelling in the positive x-direction, the wave equation can be written as
$y(x,t) =A \sin (kx-\omega t)$
where
A is the amplitude
$k= \frac{2 \pi}{\lambda}$ is the wave number
$\omega = \frac{2 \pi}{T}$ is the angular frequency

The wave in our problem has an amplitude of 
$A=8.4 cm = 0.084 m$
A wave number of (the wavelength is $\lambda=35 cm = 0.35 m$ )
$k= \frac{2 \pi}{\lambda}= \frac{2 \pi}{0.35 m}= 18 m^{-1}$
and an angular frequency of (the period is T=1.2 s)
$\omega = \frac{2 \pi}{T}= \frac{2 \pi}{1.2 s}=5.2 s^{-1}$

So, if we put this numbers into the equation, we find (in SI units):
$y(x,t)=(0.084) \sin (18 x - 5.2 t)$