Question

The speed of sound at 0°C is 331.5 m/s. Calculate the speed of sound in the room at 20.0°C.

Answer 1

The speed of sound is defined as the rate wherein pressure waves would move through a certain medium. From the kinetic theory, we know that c is equal to square root of dP/dρ where c is the speed of sound. From the ideal gas law, we have P = ρRT/M from the expression PV = nRT. Then, it follows that dP/dρ = RT/M = (Rm) (T) where Rm is the specific gas constant.

From the problem statement, we can calculate as follows:

Rm = c^2/T = 331.5^2 / (273.15+0) = 402.3 J/kg.K

Next, at the new temperature, we calculate the speed of sound as follows:

c = squareroot((Rm)T) = squareroot((402.3)(273.15+10)) = 337.5 m/s

Answer 2

v = 343.5 m/s

Step-by-step explanation:

As we know that speed of sound at a given temperature "t" is given by the formula

`v = 331.5 + 0.6 t`

now we know that

if t = 0 degree Celsius

then the speed of sound will be

v = 331.5 m/s

now at t = 20 degree Celsius

`v = 331.5 + 0.6(20)`

`v = 343.5 m/s`

so the speed will be 343.5 m/s