A 100 -Hz pure tone at a \(70-\mathrm{dB}\) sound level and a \(1,000-\mathrm{Hz}\) pure tone at the same sound level are heard separately. Do they sound equally loud? If not, which is louder, and why?

Loudness is a subjective measure of how a sound is perceived by human ears. It depends on both the sound level (measured in decibels, dB) and the frequency of the sound. The human ear is more sensitive to some frequencies than others, so two sounds with the same sound level but different frequencies may not be perceived as equally loud.

To understand how the human ear perceives loudness, we can consider the Fletcher-Munson curves, also known as equal-loudness contours. These curves represent the perceived loudness of sounds as a function of frequency and sound level. They are derived from experimental data and are used to determine how loud a sound will be perceived at a given frequency and sound level.

Now that we understand the concept of loudness and the equal-loudness contours, we can use them to compare the perceived loudness of the two given tones. Since both tones have the same sound level (70 dB), we need to find the Fletcher-Munson curve for 70 dB and use it to compare the loudness of the two tones at 100 Hz and 1000 Hz. Referring to the Fletcher-Munson curves, we can see that at 70 dB, the curve indicates the following: - For the 100 Hz tone: The perceived loudness is slightly lower than the actual sound level (70 dB), as the curve dips down for low frequencies. - For the 1000 Hz tone: The perceived loudness is very close to the actual sound level (70 dB), as the curve remains relatively flat around this frequency range.

Based on our comparison using the Fletcher-Munson curves, we can conclude that the 1000 Hz tone will sound louder than the 100 Hz tone, even though they both have the same sound level. This is because the human ear is more sensitive to frequencies around 1000 Hz, which causes sounds at this frequency to be perceived as louder than sounds with lower frequencies, such as the 100 Hz tone.