A bat emits a sound whose frequency is 83.6 kHz. The speed of sound in air at 20.0 oC is 343 m/s. However, the air temperature is 36.0 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
See Related Questions: tue,1-15-13,11:38am.
To find the wavelength of the sound, we first need to calculate the speed of sound in air at the given temperature of 36.0°C.
The speed of sound in air can be calculated using the formula:
v = sqrt(gamma * R * T),
where:
- v is the speed of sound,
- gamma is the adiabatic index for air (approximately 1.4),
- R is the molar gas constant (approximately 8.31 J/(mol·K)),
- T is the temperature in Kelvin.
Converting the temperature from °C to Kelvin:
T (in K) = 36.0 + 273.15 = 309.15 K.
Substituting the values into the formula:
v = sqrt(1.4 * 8.31 * 309.15).
Calculating the value of v will give us the speed of sound in air at 36.0°C.
Next, we can use the formula for the wavelength of sound:
wavelength = v / frequency.
Substituting the values of v (speed of sound at 36.0°C) and the given frequency (83.6 kHz = 83.6 × 10^3 Hz), we can calculate the wavelength.