Explanation:
It is given that,
Wavelength of a wave, [tex]\lambda=35\ cm=0.35\ m[/tex]
Amplitude, [tex]A=8.4\ cm[/tex]
Period of the wavelength, t = 1.2 s
The wave is traveling in a string in the positive x direction. We need to write the wave equation for this conditions.
The general equation of the wave when it is traveling in +x direction is given by :
[tex]y=A\sin(kx-\omega t)[/tex]
A is amplitude
k is propagation constant
[tex]k=\dfrac{2\pi}{\lambda}\\\\k=\dfrac{2\pi}{0.35}\\\\k=17.95\ m^{-1}\approx 18\ m^{-1}[/tex]
[tex]\omega[/tex] is angular frequency
[tex]\omega=\dfrac{2\pi}{T}\\\\\omega=\dfrac{2\pi}{1.2}\\\\\omega=5.23\ s^{-1}[/tex]
So, the wave equation is given by :
[tex]y(x,t)=(0.084) \sin (18 x - 5.2 t)[/tex]
Hence, this is the required solution.
