# Description of a wave

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1. Sep 4, 2015

### Nishikino Maki

1. The problem statement, all variables and given/known data
A simple harmonic wave train of amplitude 3 cm and frequency 200 Hz travels in the +ve direction of x-axis with a velocity of 20 m/s. Calculate the displacement, velocity, and acceleration of a particle situated at 50 cm from the origin at t = 2 s.

2. Relevant equations
I used $y(x, t) = Acos(2\pi f(\frac{x}{v}-t))$

3. The attempt at a solution
Plugging in the values into the above equation, I got $y(0.5, 2) = 0.03cos(400\pi (\frac{.5}{20} - 2))$, which evaluates to 0.0236 m. However, the book says the answer is 0.02523 m.

This is marked as an easy question and is one of the first ones, so I think that I'm missing something basic?

2. Sep 4, 2015

### haruspex

You need to be a bit careful evaluating trig functions of large angles. The series expansions used by calculators get rather inaccurate. Instead, first reduce the angle to something less than 2 pi. I think you'll find both your answer and the given answer rather inaccurate!

3. Sep 4, 2015

### Nishikino Maki

Part of my confusion lies in whether I should be in radians or degrees - the examples in the book all use radians, but when I evaluated the above, I got $cos(-790\pi)$, or 1. Changing the angle to something less than 2$\pi$ still gets me 1.

When I use degrees, I get 0.0236, which is closer to 0.02523. I plugged the expression into Wolfram-Alpha, which got me the same as the one on my calculator. Changing the angle to something less than 360 degrees got me 0.0271.

4. Sep 4, 2015

### haruspex

It gives you 1 for the value of the cos function, but you still have to multiply by A.

5. Sep 5, 2015

### rude man

I got the same answer as you.
BTW the problem should state that the wave is inded ~ cos(kx - wt) and not something like cos(kx - wt + φ), φ ≠ 0.
Always assume radians. And always assume natural instead of base-10 logs. Calculus falls apart otherwise!

6. Sep 5, 2015

### haruspex

Then you must be using a calculator that truncates the precision of pi at the same point. The right answer is clearly 0.03m.

7. Sep 5, 2015

### rude man

Not truncate. Round off.
But yes, score one for the Aussies. Again, only if the wave is cos(kx - wt + φ), φ = 0 assumed. The problem is not clearly stated.