Sound Intensity: dB vs dB(A) - What's the Difference?

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Sound intensity can be measured using two scales: dB and dB(A). The dB(A) scale adjusts for human hearing sensitivity, particularly emphasizing frequencies between 2,000 and 4,000 Hz, which are more damaging to hearing due to resonance in the ear canal. This means that sound intensity meters using dB(A) provide a weighted measurement that reflects potential hearing damage more accurately than the standard dB scale. The exact mathematical relationship between the two scales is not clearly defined in the discussion. Understanding these differences is crucial for assessing sound exposure and its effects on hearing health.
EIRE2003
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sound intensity level can be measured in dB & dB (A). What is the difference between the 2 scales?
 
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I think dB(A) is average decibel levels.
 
The dB (Adjusted) scale takes into account the fact that the frequencies between 2,000 and 4,000 Hz cause resonance in the human ear canal and so are more damaging to our hearing. Sound intensity level meters which use the dB (A) scale therefore give these frequencies a certain weighting when they are detected because higher frequencies such as 5,000 Hz would actually be less damaging to the ear due to lack of resonance in the ear canal. However I have no idea what the exact mathematical link between the two scales is, sorry.
 
See this: http://www.safetyline.wa.gov.au/institute/level2/course18/lecture54/l54_09.asp
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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