Chapter 6: Problem 32

A \(100-\mathrm{Hz}\) 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?

Short Answer

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Answer: The 1,000 Hz pure tone at a 70 dB sound level is perceived to be louder than the 100 Hz pure tone at the same sound level. This is because the human ear is more sensitive to the frequency of 1,000 Hz than to 100 Hz, as illustrated by the equal loudness contours (e.g., Fletcher-Munson curves).

Step by step solution

Understanding loudness

Loudness is perceived differently for different frequencies at the same sound level. This is due to the fact that the human ear is more sensitive to certain frequencies. The relationship between frequency and perceived loudness is described by equal loudness contours.

Using equal loudness contours

Equal loudness contours are a series of curves that represent the loudness levels of different frequencies at which the human ear perceives them to be equally loud. To understand the relative loudness of our given pure tones, we have to refer to an equal loudness contour graph or chart, such as the widely recognized "Fletcher-Munson" curves.

Locate the given pure tones on the equal loudness contour graph

On the Fletcher-Munson graph, we should locate the points representing the two given pure tones - a 100 Hz tone at 70 dB and a 1,000 Hz tone at 70 dB.

Compare the loudness of the given pure tones

According to the Fletcher-Munson curves, the equal loudness contour for 70 dB implies that the 1,000 Hz pure tone would sound louder than the 100 Hz pure tone at the same sound level. This is because the human ear is more sensitive to the frequency of 1,000 Hz than to 100 Hz, and thus perceives it to be louder even though the sound level is the same.

Conclusion

The 1,000 Hz pure tone at a 70 dB sound level is perceived to be louder than the 100 Hz pure tone at the same sound level. This is due to the frequency-dependent sensitivity of the human ear, which is illustrated by the equal loudness contours (e.g., Fletcher-Munson curves).

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A \(100-\mathrm{Hz}\) 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?

Short Answer

Step by step solution

Understanding loudness

Using equal loudness contours

Locate the given pure tones on the equal loudness contour graph

Compare the loudness of the given pure tones

Conclusion

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