{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

FTHomewor - Physics IV Homework due 3/2 It is well known...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics IV Homework due 3/2 It is well known that the tone quality (harmonic content) of a vibrating string depends on where and how it is plucked. Consider a string of length L which is fixed at both ends and which is plucked in the center. Consider a pluck with corresponds to a simple displacement with no initial velocity of the string. The wave equation is: 2 2 2 2 2 x f c t f = where y=f(x,t) is the displacement of the string. The initial conditions are f(0<x<L/2,0)=2Hx/L ; f(L/2<x<L,0)=2H(L-x)/L and 0 ) 0 , ( = t x f . 1) Use a Fourier sine series to represent the wave function and find the natural frequencies of the string. 2) What time dependence must the n f have in order to satisfy both the wave equation and the initial condition on the time derivative? 3) Perform the projection integrals on the initial displacement to determine the amplitude of the n f ’s. Hint; integrate by parts when you have the integral of x*sin(kx). 4) Write down the full solution to the wave equation f(x,t) which satisfies the initial conditions. 5) What is the relative amplitude of the even harmonics compared to the odd harmonics
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern