Answer to Question #167430 in Quantum Mechanics for Kipkirui Emmanuel

Question

A wave is travelling in the negative direction has a frequency of 40 Hz ,a wavelength of 3cm and an amplitude of 0.6cm.write the wave function y(x,t) given that y=0.6cm at x =0 and t =0.

Answer 1

The general equation of the wave function can be written as follows:

$$y(x,t)=Asin(\omega t \mp kx),$$

here, $A$ represents the amplitude of the wave, $\omega$ represents the angular frequency of the wave, $k$represents the wave number of the wave, sign minus corresponds to the wave traveling in +$x$-direction and sign plus correspond to the wave traveling in -$x$-direction.

Let's find the angular frequency and wave number of the wave:

$$\omega=2\pi f=2\pi\cdot40\ Hz=251.2\ \dfrac{rad}{s},$$ $$k=\dfrac{2\pi}{\lambda}=\dfrac{2\pi}{3\cdot10^{-2}\ m}=209\ m^{-1}.$$

Finally, we can write the wave function y(x,t):

$$y(x,t)=(0.006\ m)sin(251.2t+209x).$$