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We have a sound wave that is propagating in liquid: its displacement function is A cos(kx − 𝜔t) and its pressure function is BkA sin(kx − 𝜔t), where is A the amplitude, B is the bulk modulus, k is the wavenumber, x is the position, 𝜔 is the angular frequency (= 2πf, is the fundamental frequency), and t is the time.

a. Find the sound wave intensity as a function of 𝜔 and A

b. Find the sound wave intensity in terms of pressure information

c. Based on your findings in a and b, to increase the sound wave intensity, you will need to ________________ the amplitude, the frequency, or the pressure of the sound wave.

1 Answer

  • NCS
    Lv 7
    1 month ago
    Favourite answer

    a. intensity I = p*v

    where pressure p = B*k*A*sin(kx - ωt)

    and velocity v = A*ω*sin(kx - ωt)

    (see citation)

    so I = B*k*A²*ω*sin(kx - ωt)

    b. I = (p_max)² / 2ρv

    where p_max = B*k*A

    and ρ is the density of the liquid

    (see citation)

    c. Increase (obviously, and you'd hardly have to do the first two to know that)

    Hope this helps!

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