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Pressure equation of sound wave

  1. Jan 26, 2010 #1
    Let us consider sound (longitudinal) wave
    y=A.sin([tex]\omega[/tex]t-kx)

    See attachment for diagram

    Consider air column of length [tex]\Delta[/tex]x and cross-sectional area S at distance x from source.
    I want to derive the pressure equation of the sound wave using
    Bulk modulus, B=-[tex]\Delta[/tex]P/([tex]\Delta[/tex]V/V)
    implying [tex]\Delta[/tex]P=-B.[tex]\Delta[/tex]V/V

    But the trouble is that I am not able to select the expression for [tex]\Delta[/tex]V
    1) [tex]\Delta[/tex]V=S.y
    2) [tex]\Delta[/tex]V=S[tex]\Delta[/tex]y
    TELL ME WHICH EXPRESSION OUT OF THE TWO SHOULD I USE with EXPLANATION.
     

    Attached Files:

  2. jcsd
  3. Jan 27, 2010 #2
    I give you a hint about what I was actually thinking.

    1)[tex]\Delta[/tex]V=S.y
    It would mean that [tex]\Delta[/tex]P is the difference between the initial pressure of the volume considered and the final pressure of the same column (now volume is reduced to (V-[tex]\Delta[/tex]V) but mass(amount) remains same).

    2)[tex]\Delta[/tex]V=S.[tex]\Delta[/tex]y
    It would mean that [tex]\Delta[/tex]P is the change in pressure for a change [tex]\Delta[/tex]y
    in the length of the column.

    Which of the above does the pressure equation of sound wave denotes? Please, tell.

    NOTE: If you find any problem in understanding what I want to say, please tell.
     
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