For sound waves, the period and the frequency of a pitch are reciprocals of each other: period = s e c o n d s c y c l e and frequency = c y c l e s s e c o n d . Write an equation for each pitch. Let θ = time in seconds.Use a=1. the lowest pitch heard by elephants: 15 cycles per second.

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For sound waves, the period and the frequency of a pitch are reciprocals of each other: period   =            s      e      c      o      n      d      s              c      y      c      l      e       and frequency  =            c      y      c      l      e      s              s      e      c      o      n      d      . Write an equation for each pitch. Let   θ = time in seconds.Use a=1. the lowest pitch heard by elephants: 15 cycles per second.

lelestalis80d · Accepted Answer

Let   c be any nonzero rational number.Let       P    n   be the       n    th  th prime number.Define a sequence of nonzero rational numbers       r    n   recursively so that      r    1        r    2    ⋯      r    n    =      c          ⌊                        P          1                          P          2                ⋯                  P          n                    ⌋        .Let       a    n    =      r    n              P      n      . Then      lim          n      →      ∞            a    1        a    2    ⋯      a    n    =      lim          n      →      ∞        c  ⋅                    P        1                    P        2            ⋯              P        n                    ⌊                        P          1                          P          2                ⋯                  P          n                    ⌋        =  c  .Thus the infinite product       ∏          n      =      1        ∞        a    n   converges to   c. The product of any nonempty finite set of distinct terms is irrational, being a nonzero rational multiple of the square root of a product of distinct primes.

For sound waves, the period and the frequency of a pitch are reciprocals of each other: period =seconds/cycle and frequency =cycles/second . Write an equation for each pitch. Let theta = time in seconds. Use a=1. the lowest pitch heard by elephants: 15 cycles per second.

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