Homework 02 - HOMEWORK 2 SOLUTIONS PROBLEM – THE HEARING...

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Unformatted text preview: HOMEWORK 2 SOLUTIONS PROBLEM – THE HEARING OF A BAT : 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 M RT v γ = where γ is the ratio of heat capacities ( 4 . 1 = γ for air), is the absolute temperature in kelvins (which is equal to the Celsius temperature plus 273.15 C), M is the molar mass of the gas (for air, the average molar mass is M = 28.8 x 10-3 kg/mol), and R is the universal gas constant (R = 8.314 J/mol-K). (a) Find the wavelength of the 80.0-kHz wave emitted by the bat. ( ) ( )( ) mm 85 . 4 10 8 . 28 K 15 . 373 314 . 8 4 . 1 Hz 000 , 80 1 M RT f 1 M RT v f v mol kg 3 molK J = × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = γ = λ γ = λ = − (b) Will the bat be able to locate the moth despite the darkness of the night? Yes, because the wavelength is smaller than the size of the moth. (c) How long after the bat emits the wave will it hear the echo from the moth? s 10 15 . 5 t 2 t s 10 58 . 2 388 m . 1 t 3 total 3 s m − − × = = × = = PROBLEM – THE ELECTROMAGNETIC SPECTRUM (A) Which of the following statements correctly describe the various forms of EM radiation listed above? (A) Which of the following statements correctly describe the various forms of EM radiation listed above?...
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