40. Review. A block with a speaker bolted to it is connected to a spring having

Question

40. Review. A block with a speaker bolted to it is connected to a spring having spring constant k and oscillates as shown in Figure P17.39. The total mass of the block and speaker is m, and the amplitude of this unit’s motion is A. The speaker emits sound waves of frequency f. Determine (a) the highest and (b) the lowest frequencies heard by the person to the right of the speaker. (c) If the maximum sound level heard by the person is ß when the speaker is at its closest distance d from him, what is the minimum sound level heard by the observer?

I understand a and b but not c

Explanation / Answer

The maximum sound level heard by person is

Let the minimum soud level heard by person be min

The maximum sound level

                  = 10dBlog(I/I0)

    Since the intensity I = P/4r^2

The maximum intensity level occurs at rmin = d

the minium intensity level occurs at rmax = rmin + 2A

Thus

   max - min = 10dBlog(P/4I0rmin^2) - 10dBlog(P/4I0rmax^2)

                       = 10dBlog [(P/4I0rmin^2) - (4I0rmax^2/P)]

                       = 10dB log( rmax^2 / r min^2)

   Therefore the minimum sound level

             min = max - 10dB log( rmax^2 / r min^2)

                      = - 10dB log( (d+2A)^2 / d^2)

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