A bat emits a sound with a frequency of 91 kHz. The air temperature is 35 degrees celsius. What is the wavelength of the sound? Show your process.

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Irving HeathcoteLv2

2 Apr 2019

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A bat emits a sound whose frequency is 82.2 kHz. The speed of sound in air at 20.0 oC is 343 m/s. However, the air temperature is 37.3 oC, so the speed of sound is not 343 m/s. Assume that air behaves like an ideal gas, and find the wavelength of the sound.

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 the 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.

where the ratio of heat capacities ( 1.4 for air), T is the absolute temperature in kelvins (which is equal to the Celsius temperature plus 273.15 C), 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 of the 80.0-kHz wave emitted by the bat.

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

limegoldfish893

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 the 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= sqrt (γRTM), 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=28.8×10−3kg/mol), and R is the universal gas constant (R=8.314J⋅mol−1⋅K−1).

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

Express your answer in millimeters.

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.