Understanding Wave Displacement: Frequency, Wavelength, and Speed Calculation

[Dark Visitor]

The displacement of a wave traveling in the positive x-direction is y(x,t) = (3.5 cm)cos(2.7x - 124t), where x is in m and t is in sec. What are the (a) frequency, (b) wavelength (in m), and (c) speed (in m/s) of this wave?



I don't know how to do this problem at all. I could use some help beginning and solving this problem. Thanks. I don't know how to do harmonics very well.

 

[diazona]

For starters, what do you know about frequency, wavelength, and speed in general?

 

[Dark Visitor]

They are all linked in the equation:

v = $$\lambda$$f

 

[Dark Visitor]

The only thing I don't get is how to find any of them if they are all linked with one equation.

 

[Dark Visitor]

Well, after doing the math (considering I did this right, or I hope I did), I got:

y(x,t) = Acos((2$$\pi$$/$$\lambda$$)x $$\pm$$ (2$$\pi$$/T)t)

which led me to

(a): 124 = 2$$\pi$$/T
T = 2$$\pi$$/124 = .05067

f = 1/T = 1/.05067 = 19.74

(b): 2.7 = 2$$\pi$$/$$\lambda$$
$$\lambda$$ = 2$$\pi$$/2.7 = 2.33 m

(c): v = $$\lambda$$f
v = (2.33 m)(19.74) = 45.99 m/s



Please tell me if and where I am wrong, or tell me if that is correct. Bold are the answers.

 

[MaxL]

That's what I got!

 

[Dark Visitor]

Well, do you think we are right? I sure as heck hope so!

 

[MaxL]

Haha, yeah, we're right.