Horseshoe bats use the Doppler effect to determine their location. A horseshoe bat flies toward a wall at a speed of 19 m/s while emitting a sound of frequency 37 kHz. What is the beat frequency between the emission frequency and the echo?

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Cortez Hughes · Accepted Answer

The bat emits a sound which is reflected off the wall. This then interferes with the incoming signal to produce beats.The incoming signal is &quot;Doppler Shifted&quot; twice because it has been reflected off a wall to which the bat is moving.To get the beat frequency you find the difference between the two frequencies.I will assume that at 20 degC the speed of sound v is 343.7m/sThe beat frequency between a transmitted signal and a reflected signal off a moving object is:      f          r      e      f      l      e      c      t      e      d        −      f          t      r      a      n      s      m      i      t      t      e      d        =  △  f  =            2              v                  t          a          r          g          e          t                      v    ∗  fIn relative terms we can consider the wall to be moving towards the bat.  ∴  △  f  =            2      ×      19        343.7    ×  37  ×      10          3        △  f  =  4.09  ×      10          3        H  zPolice radar guns measure vehicle speeds like this.

Horseshoe bats use the Doppler effect to determine their location.

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