A moth of length 1.0 cm is flying about 1.0 m from a bat when the bat emits a so

Question

A moth of length 1.0 cm is flying about 1.0 m from a bat when the bat emits a sound wave at 80.0 kHz. The temperature of air is about 10.0° C. To sense the presence of the moth using echolocation, the bat must emit a sound with a wavelength equal to or less than the length of the insect The speed of sound that propagates in an ideal gas is given by where ? is the ratio of heat capacities ? 1.4 for air is the absolute temperature in kelvins (which is equal to the Celsius temperature plus 273 15°C) Mis the molar mass of the gas (for air, the average molar mass is M = 28.8 x 10 3 kg/mol) and Ris the universal gas constant R-8.314 J-mol 1-K 1).

Explanation / Answer

Speed of the wave

V=sqrt[1.4*8.314*(273.15+10)/(28.8*10-3)]

V=338.28 m/s

To hear the echo ,the sound wave must travel back and forth .so total distance is 2m

t=2/338.28

t=5.91 ms

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