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Title: GR8677.004
Post by: conantee on December 31, 2009, 03:48:46 AM
4. The equation y = A \sin 2 \pi (\frac{t}{T} - \frac{x}{\lambda}), where A, T and \lambda are positive constants, represents a wave whose
(A) amplitude is 2A
(B) velocity is in the negative x-direction
(C) period is \frac{T}{\lambda}
(D) speed is \frac{x}{t}
(E) speed is \frac{\lambda}{T}


Title: Re: GR8677.004
Post by: conantee on December 31, 2009, 03:59:33 AM
If you are familiar with wave function like this, it is relatively easy problem. If not, you can eliminate some irrelevant choices.
(C) is wrong since T is already in time unit (remember that number in sine/cosine function is phase which has no unit) while \lambda is length unit.
(D) is also wrong since at t=0 the speed goes to infinity. (How the wave runs to infinity in no time?)
(A) is wrong. You can show it by knowledge of sine function. This is not even the subject of physics.

Now, we have only (B) and (E). This is the point you need true knowledge of wave function. You can draw a graph of y(x) at time t=0 and t=T/4 to see the direction of the wave. However, according to the different signs of x and t, it is known that the wave propagates to positive direction.

Another way to approach it, T is called period (amount of time to make a wave repeat itself), and \lambda is called wavelength (amount of length to make a wave repeat itself). By high school physics, the ratio of wavelength and period is the speed of wave.

The correct answer is (E). By stats, 55 of 100 people got the right answer.