GREPhysics.NET: GR8677 #4

GR8677 #4

Problem

GREPhysics.NET Official Solution

Wave Phenomena $\Rightarrow$ }Wave Equation

Perhaps this formula is more familiar: $y=A\sin(\omega t - k x)$ . But then again, they define the familiar quantities $k$ and $\omega$ for you in theirs...

(A) The amplitude is A. (Recall that the amplitude of $y=sin(x)$ is just 1, not 2.)

(B) How exactly does the argument of $\sin$ make it a traveling wave? Well, a traveling wave keeps the same waveform at all times. Thus, the overall argument has to be constant. $\omega t - kx = constant\Rightarrow x \propto - constant +\omega t$ . This looks like the old high school kinematics equation $x=-constant + vt$ . In fact, it's basically the same thing. That high school equation describes a particle going in the positive x-direction. So does this equation.

(C) Dimensions don't match. Period has units of time, not units of time/meter.

(D) The speed of the wave is $v=\lambda/T$ . From the kinematics explanation explained in (B), the velocity of the wave is obviously $v=\frac{\omega}{k}=\frac{2\pi\lambda}{2\pi T}$

(E) True. See (D) and (B).

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Comments

anmuhich
2009-03-19 08:39:59

Or you just know that for a sine wave the velocity is just the wavelength over the period.

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icelevistus
2007-09-27 16:29:19

The only variables/constants we can assume the units of are x and t. All others are unspecified, despite what convention suggests.

Thus, the application of dimensional analysis for eliminating answers only works for D.

icelevistus
2007-09-27 16:30:20

Never mind, the units are implicit for the sin argument to be unitless.

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