Question

The sound level of a certain sound is at 85 dB. This sound has a frequency of 1250 Hz.. It travels in a copper beam. The density of copper is 8.92 g/cm3 . Its elastic-modulus is 11x1010 Pascals . a) Find the speed of sound inside the copper beam and the intensity of this sound-wave.   Answer: v=3511 m/s; I=3.16E-4W/m2 ; ∆P=141Pa;

b) Find the maximum speed of the vibrating copper particles. Answer: smax=5.74E-10m; vmax=4.5E-6m/s

Answer 1

the speed of sound in copper is:

   v = sqrt[B/rho] = sqrt[11x10¹⁰ / 8920] = 3511 m/s

the intensity level of the sound wave is,

   L = 10log[I/I0]

   85 = 10log[I/10^-12]

hence, the intensity: I = 3.16E-4 W/m2

the angular frequency is:

     ω = 2πf = 2 x π x 1250 = 7850 rad/s,

The amplitude of the vibrating particles:

    Smax = [1/w]sqrt[2I/rho*v] = 5.74E-10 m

the maximum speed is,

    vmax = ωs_max = 4.5E-6 m/s