If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level (in dB) of 1000 flies at that distance, assuming interference has a negligible effect? Give your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

We start by noting the given: a single large housefly at 3.0 m away produces a sound level of 40.0 dB. If we have 1000 flies at the same distance, and interference is negligible, the intensities add up.

Key idea: sound level in decibels is related to the total acoustic intensity by L = 10 log10(I / I0). If you have N independent sources emitting the same intensity I1 at the same location, the total intensity is I_total = N * I1, so the total level is L_total = 10 log10(N * I1 / I0) = 10 log10(N) + 10 log10(I1 / I0) = 10 log10(N) + L1, where L1 is the level from one source.

Here, N = 1000 and L1 = 40 dB. Therefore, L_total = 10 log10(1000) + 40 = 10 * 3 + 40 = 30 + 40 = 70 dB.

Thus, the noise level of 1000 flies at the same distance, with negligible interference, is 70 dB. The calculation relies on the linear additivity of intensities for independent sources and the logarithmic nature of decibels.

If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level (in dB) of 1000 flies at that distance, assuming interference has a negligible effect? Give your answer to the nearest whole number.数值题

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