So the bell can barely be heard at a distance of one mile.Ī speaker at the north end of a round football stadium emits a sound at a single frequency. Therefore to drop by a factor of 100, the distance must increase by a factor of 10. The sound from the bell expands outward spherically, so the intensity drops off according to the inverse-square law. The bell can barely be heard at the threshold of hearing, which is \(0\ dB\), which means that the decibel level can afford to drop by \(20\ dB\), and the intensity can drop by two factors of 10 (i.e. The decibel scale is logarithmic, which means that every time the decibel level changes by \(10\ dB\), the intensity changes by a factor of 10. at what distance does the bell become barely audible)? Assume that there is negligible energy dissipated from the sound wave due to obstacles and the atmosphere. If the loudness of the bell heard by villagers in the town \(500\ ft\) (about 1/10 mile) from the tower is \(20\ dB\), then about how far from the tower does the sound carry (i.e. Note that the threshold of hearing results in zero decibels, while the pain threshold occurs at \(120\ dB\).Ī medieval village has a bell located in a tower in its central square which is rung to warn the townspeople of emergencies, such as raiding parties from nearby regions. It is traditional to multiply this by number by 10, so that the unit describing the loudness is decibels. The number yielded by just the logarithm of the ratio is described as the number of "bels" of the loudness of the sound.
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