As Barak suggested in his comment, the perceptible sound quality I was actually referring to in yesterday’s post is sound pressure (the actual pressure of a sound against the ear), rather than loudness, which is a convenient logarithmic scale of perception. Barak, thanks for pointing that out.<\/p>\n
Sound pressure — the external phenomenon our ears can perceive — falls off as 1\/distance, rather than 1\/distance2<\/sup>. Why is that?<\/p>\n Well, sound waves consist of regions of air that are acting against each other like little springs. Each air particle is actually spinning in a kind of circle. One dimension of this circle is how rarified or compressed the air is. The other dimension of the circle is how fast each air particle is moving. <\/p>\n When you clap your hands together with four times as much energy, the pressure variation becomes twice as big, and each air particle also moves twice as fast: 2 × 2 = 4. You can think of the energy as the area of this pressure\/velocity circle: As particles spin around in this circle with a given frequency, the area of the circle (proportional to pressure × velocity) tells us how much energy the particle has.<\/p>\n By the way, how may times per second each particle spins around in its energy circle is indeed the frequency of the sound. For example, the sound from a standard A-pitch tuning fork makes the air particles spin around in their little pressure\/velocity circles exactly 440 times per second.<\/p>\n The energy you cause by clapping your hands indeed drops off as 1\/distance2<\/sup>, but our ears can only perceive one dimension of this spinning energy — the pressure axis. The other dimension consists of velocity<\/i> — how fast the air moves as it rhythmically expands and contracts. Our ears cannot perceive this velocity dimension (just as, if you get hit by a baseball, you don’t feel how fast it was going, only how hard it has hit you). The part we can perceive — the pressure variation — which varies with the diameter of the energy circle, not with its area — drops off as 1\/distance.<\/p>\n","protected":false},"excerpt":{"rendered":" As Barak suggested in his comment, the perceptible sound quality I was actually referring to in yesterday’s post is sound pressure (the actual pressure of a sound against the ear), rather than loudness, which is a convenient logarithmic scale of perception. Barak, thanks for pointing that out. Sound pressure — the external phenomenon our ears … Continue reading “2 \u00d7 2 = 4”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8012"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8012"}],"version-history":[{"count":6,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8012\/revisions"}],"predecessor-version":[{"id":8017,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8012\/revisions\/8017"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8012"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}