How is the speed of sound calculated in relation to temperature?

How is the speed of sound calculated in relation to temperature?

• A. 39 x square root of temperature in Celsius
• B. 39 x square root of temperature in Kelvin
• C. 39 + square root of temperature in Celsius
• D. 39 + temperature in Kelvin

Answer: (B)

The correct calculation of the speed of sound involves using the temperature in Kelvin because the speed of sound is directly related to the absolute temperature of the air. The formula for calculating the speed of sound in air is given by: \[ c = 331.3 + (0.6 \times T) \] where \( c \) is the speed of sound in meters per second and \( T \) is the temperature in degrees Celsius. However, when considering temperature in the context of gas laws and thermodynamic principles, it's essential to convert temperature to an absolute scale, which is measured in Kelvin. To find the speed of sound more accurately, the square root of the absolute temperature in Kelvin can be used in calculations as follows: \[ c = 39 \times \sqrt{T(K)} \] This consideration for temperature in Kelvin ensures that the calculations reflect the fundamental properties of gases, where absolute zero corresponds to the lowest thermal energy state. Using Celsius directly in a square root function would not yield a correct expression for the speed of sound, hence the preference for Kelvin in formal calculations. Overall, temperature in Kelvin provides the necessary linkage between thermal energy and the molecular motion responsible for sound propagation.

The correct calculation of the speed of sound involves using the temperature in Kelvin because the speed of sound is directly related to the absolute temperature of the air. The formula for calculating the speed of sound in air is given by:

[ c = 331.3 + (0.6 \times T) ]

where ( c ) is the speed of sound in meters per second and ( T ) is the temperature in degrees Celsius. However, when considering temperature in the context of gas laws and thermodynamic principles, it's essential to convert temperature to an absolute scale, which is measured in Kelvin.

To find the speed of sound more accurately, the square root of the absolute temperature in Kelvin can be used in calculations as follows:

[ c = 39 \times \sqrt{T(K)} ]

This consideration for temperature in Kelvin ensures that the calculations reflect the fundamental properties of gases, where absolute zero corresponds to the lowest thermal energy state. Using Celsius directly in a square root function would not yield a correct expression for the speed of sound, hence the preference for Kelvin in formal calculations.

Overall, temperature in Kelvin provides the necessary linkage between thermal energy and the molecular motion responsible for sound propagation.