Question

What is the speed of sound, in FT/S, if the air temperature is,

A: 0.0C

B: 23.6C FT/S

C: 45.1C Ft/S

D: 85.6 C FT/S

I have 4 Boxes to fill that are empty, and 3 attempts to do this problem, someone please help me.

Answer 1

Solution :-

Formula to calculate the speed of sound is as follows

c=(*R*T/M)^1/2

= adiabatic index air = 1.4

R= gas constant 4.184 J/mol K

T= temperature in kelvin

M= molar mass of air in kg (0.0289645 kg/mol)

c= speed of sound.

Lets calculate the speed of sound for the given temperatures

#1) 0.0 C + 273.15 = 273.15 K

c=(*R*T/M)^1/2

c=(1.4*8.314 J per mol K * 273.15 K / 0.0289645 kg/mol)^1/2

c=331.3 m/s

lets convert the m/s to ft/s

331.3 m/s* 3.28084 ft/1 m = 1086.7 ft/s

Therefore the speed of sound is 1086.7 ft/s

#2) 23.6 C +273.15 = 296.75 K

c=(*R*T/M)^1/2

c=(1.4*8.314 J per mol K * 273.15 K / 0.0289645 kg/mol)^1/2

c=345.3m/s

lets convert the m/s to ft/s

345.3 m/s* 3.28084 ft/1 m = 1133 ft/s

Therefore the speed of sound is 1133 ft/s

#3)45.1 C + 273.15 C= 318.25 K

c=(*R*T/M)^1/2

c=(1.4*8.314 J per mol K * 318.25 K / 0.0289645 kg/mol)^1/2

c=357.6 m/s

lets convert the m/s to ft/s

357.6 m/s* 3.28084 ft/1 m = 1173 ft/s

Therefore the speed of sound is 1173 ft/s

#4)85.6 C +273.15 = 358.75 K

c=(*R*T/M)^1/2

c=(1.4*8.314 J per mol K * 358.75 K / 0.0289645 kg/mol)^1/2

c=379.7 m/s

lets convert the m/s to ft/s

379.7 m/s* 3.28084 ft/1 m = 1245 ft/s

Therefore the speed of sound is 1245 ft/s