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~christina~

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**[SOLVED] sinusoidal wave (not sure what to do for the last part)and have test tommoro**

**1. Homework Statement**

A sinusoidal wave representing transverse oscillations on a string has the wave function

[tex]y(x,t)= (0.40m)cos[(10.0\frac{rad} {s})t- 5.00\frac{rad} {m}x][/tex]

The linear mass density of the string is 0.015kg/m

a) what is the phase velocity of the wave, the tension in the string and the period of oscillation?

b) Find the transverse velocity and acceleration of the wave when x= 3.60m and t= 2.00s

c) If the ends of the string are fixed, a second sinusoidal wave function is given by

[tex]y(x,t)= (0.40m)cos[(10.0\frac{rad} {s})t- 5.00\frac{rad} {m}x][/tex]

travels on the string. Give a description of the resulting interference of these waves.

d) sketch the resulting wave pattern

**2. Homework Equations**

**3. The Attempt at a Solution**

for

**a) what is the phase velocity of the wave, the tension in the string and the period of oscillation?**

I think I'd use these equation:

phase velocity: [itex]v=\omega /k [/itex]

tension: [itex]v= \sqrt{T/ \mu}[/tex]

**[itex]\omega= 2\pi / T[/itex]**

*period of oscillation: (not sure what the period of oscillation is though)***b) Find the transverse velocity and acceleration of the wave when x= 3.60m and t= 2.00s**

I think I'd find the derivative of the wave equation thus having in general

[tex]v_y= \frac{d_y} {d_t} |_{x= constant} = \frac{\delta y} {\delta t}= -\omega A cos(kx-\omega t) [/tex]

**d)**

**For the last part I'm not sure how to determine what type of interference it is. I think that since one wave is + and one is - one is going to the right(-) and one to the left(+) and both have the same amplitude and such but how would I describe it?**

The funny part is that what is "different direction" as it pertains to the signs exactly?

In my book it shows destructive interference:(one wave up and one wave down and both coliding) HOWEVER both are going in different directions (towards each other and that's what I think of when they say "different directions but is this wrong?).

Constructive interference: (based on book) both waves are up and both collide. What's confusing is since they collide, are they from "different directions"?

The funny part is that what is "different direction" as it pertains to the signs exactly?

In my book it shows destructive interference:(one wave up and one wave down and both coliding) HOWEVER both are going in different directions (towards each other and that's what I think of when they say "different directions but is this wrong?).

Constructive interference: (based on book) both waves are up and both collide. What's confusing is since they collide, are they from "different directions"?

basically need the most help with the last part

Thank you

I'd REALLY REALLY appreciate if if someone could help me out with the last part at least.

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