Answer to Question #167430 in Quantum Mechanics for Kipkirui Emmanuel

Question #167430

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.


1
Expert's answer
2021-03-01T12:40:14-0500

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


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

here, AA represents the amplitude of the wave, ω\omega represents the angular frequency of the wave, kkrepresents the wave number of the wave, sign minus corresponds to the wave traveling in +xx-direction and sign plus correspond to the wave traveling in -xx-direction.

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


ω=2πf=2π40 Hz=251.2 rads,\omega=2\pi f=2\pi\cdot40\ Hz=251.2\ \dfrac{rad}{s},k=2πλ=2π3102 m=209 m1.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).y(x,t)=(0.006\ m)sin(251.2t+209x).

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment