The toadfish makes use of resonance in a closed tube to produce very loud sounds. The tube is its swim bladder, used as an amplifier. the sound level of this creature has been measured as high as 97 dB.
(a) Calculate the intensity of the sound wave emitted.
(b) What is the intensity level if seven of these fish try to imitate seven frogs by saying "Budweiser" at the same time?
Sound intensity level in dB of a sound at intensity I is defined
L = 10∙log₁₀( I/I₀ )
with I₀ = 10⁻¹²W/m² threshold of hearing
I = I₀ ∙ 10^( L/10 )
So a sound with a level of 97dB has an intensity of
I = 10⁻¹²W/m² ∙ 10^( 97/10 )
Because sound intensity level is a logarithmic scale, multiplying the sound intensity by some factor corresponds to an addition of some other factor to the level.
Let L' be the SIL associated with r times of original intensity I and level L, i.e.:
L' = 10∙log₁₀( r ∙ I/I₀)
because log(a∙b) = log(a) + log(b)
L' = 10∙log₁₀(r) + 10∙log₁₀( I/I₀ )
L' = 10∙log₁₀(r) + L
So seven fish sounding together cause a sound intensity level of:
L' = 10∙log₁₀(7) + 97
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