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~christina~

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## Homework Statement

As a wave passes through any element of a stretched string under tension

**T**, the element moves perpendicularly to the wave's direction of travel. By applying the laws of physics to the motion of the element, a general differential equation, called the linear wave equation, can be derived.

a) Use a small string segment of length)

**x**and mass

**m**= [tex]\mu [/tex])x ([tex]\mu [/tex] is the linear mass density of the string)to derive the linear wave equation. List all physics principles and assumptions used in your derivation.

b) Waves propagate to the right along a string that has tension

**T= 2.1N**and mass per unit length [tex] \mu= 150g/m [/tex] The maximum displacement onthe string is 12mm. At t= 0 wave peaks occur at

**x= 5.0cm**and every

**17cm**thereafter. IN SI units, write the wave function for this system in the form [tex] y(x,t)= Asin(kx \pm \ometa t + \phi) [/tex]. This wave function must include the correct sign in front of [tex]\omega[/tex] and the numerical values for A, k, [tex]\omega[/tex], and [tex] \psi [/tex]

c) Standing waves are produced when ideal harmonic waves also propagate to the left along this string. Find the wave function for these standing waves.

d) Show that the wave function for the standing waves satisfies the linear wave equation.

## Homework Equations

not so sure about equations..

v= [tex]\sqrt {T/m} [/tex]

Other than that an I'm lost.

## The Attempt at a Solution

First of all how do you do partial derivatives...

I really need someone to get me started and help me through this problem...

I'm not too good at derivatives so I'll have to look up that but partial derivatives are new to me totally. I've never seen them even though I took Calculus 2 already. I'll look up partial derivative and such but I still need help :sad:

Thank you very very much.

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