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A single goose sounds a loud warning when an intruder enters the farmyard. Some distance from the goose, you measure the sound level of the warning to be 88.0 dB. If a gaggle of 32 identical geese is present, and they are all approximately the same distance from you, what will the collective sound level be if they all sound off simultaneously? Neglect any interference effects.

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Answer:

Explanation:

The application of beer lambert law comes in;

  • L = 10Log (I/Io)
  • given loudness = 88.0DB
  • For 32 identical geese, loudness is  ; I' = 32I
  • L' = 10Log(32I/Io)
  • L' = 10 [ Log32 + Log (I/Io)]
  • Plugging the values ; L' = 10Log32 + 88
  • = 103.05DB

The collective sound level if they all sound simultaneously is; L_32 = 154.49 dB

We are given;

Sound level; L1 = 88 dB

Number of geese; N = 32

To solve the collective sound level, we will use the formula for intensity level which is;

L = 10log(I/I_o)

where;

L is the loudness of a sound in decibels

I is the number of watts per square meter produced by the soundwave

I_o is threshold level and has a constant value = 10^(-12) w/m²

Now, intensity for 32 geese will be;

I_32 = 32I

Thus;

L_32 = 10log(32 × 88/10^(-12))

From law of logarithms, this can be expressed as;

L_32 = (10log 32) + (10 log (88/10^(-12)))

L_32 = 15.05 + 139.44

L_32 = 154.49 dB

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