Question

the softest sound a human ear can hear is at 0 db (io = 10-12 w/m2). sounds above 130 db cause pain. a particular student's eardrum has an area of a = 51 mm2.

Answer 1

The human ear can hear sounds with an intensity level as low as 0 dB (10^-12 W/m^2) and can endure up to 130 dB without long-term damage, which equates to an intensity of 1 W/m^2. Frequency greatly affects the perception of loudness, with 2000 to 5000 Hz being the most sensitive range for the human ear.

Step-by-step explanation:

The human ear is capable of detecting sounds with a wide range of intensities. The softest sound that can be heard, also known as the threshold of hearing, has an intensity of 10-12 W/m2 which corresponds to 0 dB (decibels). The eardrum of the human ear is quite small, generally about 1 cm2, and yet it is sensitive enough to respond to the minuscule energy that falls upon it at this lowest audible intensity. At the other extreme, intensities of about 1 W/m2, or around 130 dB, can cause pain and potentially damage to the ear. Frequency also plays an important role in how we perceive loudness, with the ear being most sensitive to frequencies between 2000 to 5000 Hz. Such sensitivity is even more impressive considering that at the threshold of hearing, air molecules vibrate over distances of less than one molecular diameter, and the gauge pressures are less than 10-9 atmosphere (atm).

Answer 2

Humans can hear sounds ranging from 0 dB to levels that cause pain above 130 dB. The lowest intensity perceivable is 10⁻¹² W/m². Using an analogy for measurement, if 1 mm was the smallest distance, the proportional largest distance would be one billion meters.

Step-by-step explanation:

The student's question involves understanding the range of hearing in humans and relating it to sound intensity levels in decibels (dB) and watts per meter squared (W/m²). The decibel level represents the loudness of a sound, and humans are capable of hearing sounds from 0 dB (threshold of hearing) to levels that cause pain above 130 dB. The eardrum, despite having a small area, can detect very low intensities of sound. The sound intensity that can be heard by the human ear without pain ranges between the threshold of hearing at 10⁻¹² W/m² and the pain threshold at around 1 W/m².

To address the example provided, let's imagine using an instrument capable of measuring a range of distances similar to those of sound intensities the human ear can detect, which spans a trillionfold range. If the smallest distance measurable was 1 millimetre (1 mm), then the largest distance that could be measured would be 10¹² meters (10¹² mm), which is equivalent to one trillion millimetres or one billion meters.