1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Determing wavelength of sound wave from steel string

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data

    A 120 cm-long steel string with a linear density of 1.2 g/m is under 100 N tension. It is plucked and vibrates at its fundamental frequency.

    What is the wavelength of the sound wave that reaches your ear in a 20 [tex]\circ[/tex]C room?

    2. Relevant equations

    Fundamental Frequency

    f1 = [tex]\frac{v}{2L}[/tex]

    Fundamental Frequency of a stretched string

    f1 = [tex]\frac{1}{2L}[/tex][tex]\sqrt{\frac{T_s}{\mu}}[/tex]

    Wavelengths of standing wave modes

    [tex]\lambda[/tex]m = [tex]\frac{2L}{m}[/tex]

    [tex]\lambda[/tex]m = [tex]\frac{v}{f_m}[/tex]

    3. The attempt at a solution

    I solved fundamental frequency as 143.3 then used

    [tex]\lambda[/tex]m = [tex]\frac{v}{f_m}[/tex] to find the wavelength.

    I also tried solving for fundamental frequency using

    f1 = [tex]\frac{1}{2L}[/tex][tex]\sqrt{\frac{T_s}{\mu}}[/tex]

    All of my answers have been incorrect. Please help!
     
  2. jcsd
  3. Feb 7, 2010 #2
    Speed of wave in string: v = [tex]\sqrt{\frac{T_s}{\mu}}[/tex]
    Ts = 100N​
    [tex]\mu[/tex] = 0.0012kg/m​
    v = 288.7​

    Fundamental Frequency: F0 = [tex]\frac{v}{\lambda_0}[/tex]
    [tex]\lambda[/tex]0 = 2L = 2*1.2​
    [tex]\lambda[/tex]0 = 2.4​

    f0 = [tex]\frac{\sqrt{\frac{T_s}{\mu}}}{2L}[/tex]

    In the air:

    [tex]\lambda[/tex] = [tex]\frac{v}{f_0}[/tex]

    [tex]\lambda[/tex] = [tex]\frac{v}{\frac{\sqrt{\frac{T_s}{\mu}}}{2L}}[/tex]

    [tex]\lambda[/tex] = [tex]\frac{v2L}{\frac{\sqrt{T_s}}{\mu}}[/tex]

    [tex]\lambda[/tex] = [tex]\frac{344m/s * 2.4}{288.7}[/tex] = 2.86
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook