Question

Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce if its sound gathering area is 900 cm(²) and the area of the eardrum is 0.500 cm(²), but the trumpet only has an efficiency of 5.00% in transmitting the sound to the eardrum?

a) 21.8 dB
b) 19.8 dB
c) 20.9 dB
d) 18.9 dB

Answer 1

The decibel increase produced by the ear trumpet is approximately 16.27 dB. This increase can be useful for individuals with hearing loss but may not be as effective as other hearing devices.

Step-by-step explanation:

To calculate the decibel increase produced by an ear trumpet, we can use the formula:
Decibel Increase (dB) = 10 * log10 (sound gathering area / eardrum area) * efficiency

Substituting the given values into the formula, we get:
Decibel Increase (dB) = 10 * log10 (900/0.5) * 0.05
Decibel Increase (dB) = 10 * log10 (1800) * 0.05
Decibel Increase (dB) ≈ 10 * 3.255 * 0.05
Decibel Increase (dB) ≈ 16.27 dB

The decibel increase found is approximately 16.27 dB. This increase can be helpful for individuals with hearing loss as it amplifies the sound and makes it easier for them to hear. However, it's important to note that the efficiency of the ear trumpet is relatively low, so the amplification may not be as significant as other hearing devices or technologies available today.