Problem: 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 v = (γRT/M)(1/2), where γ is the ratio of heat capacities (γ = 1.4 for air), T 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 = 28.8×10−3 kg/mol), and R is the universal gas constant (R = 8.314J⋅mol−1⋅K−1).a) Find the wavelength λ of the 80.0-kHz wave emitted by the bat.Express your answer in millimeters.b) How long after the bat emits the wave will it hear the echo from the moth?Express your answer in milliseconds to two significant figures.

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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 v = (γRT/M)(1/2), where γ is the ratio of heat capacities (γ = 1.4 for air), T 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 = 28.8×10−3 kg/mol), and R is the universal gas constant (R = 8.314J⋅mol−1⋅K−1).

a) Find the wavelength λ of the 80.0-kHz wave emitted by the bat.

Express your answer in millimeters.

b) How long after the bat emits the wave will it hear the echo from the moth?

Express your answer in milliseconds to two significant figures.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Sound Waves concept. You can view video lessons to learn Sound Waves. Or if you need more Sound Waves practice, you can also practice Sound Waves practice problems.

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Based on our data, we think this problem is relevant for Professor Pham's class at USF.