Question

The veloctiy of sound in air is given by the equation v=20 times the square root of 273+t where v is the velocity in meters per second and t is the temperature in degrees Celcius. Find the temperature when the velocity of sound in air is 369 meters per second. Round to the nearest degree.

Answer 1

so we just need to plug in our values and solve

`v = 20 √(273 + t)`
we are given v is 369 so we have

`369 = 20 √(273 + x)`
now we solve for x.
divide both sides by 20
square both sides
subtract 273 from both sides

`369 = 20 √(273 + x) \\ 18.45 = √(273 + x) \\ 340.40 = 273 + x \\ x = 67.4`
so a temp of about 67 degrees C

Answer 2

The velocity of sound in air is 369 meters per second at 67 degrees Celcius.

Explanation:

The veloctiy of sound in air is given by the equation

`v=20√(273+t)`

where v is the velocity in meters per second and t is the temperature in degrees Celcius.

We need find the temperature when the velocity of sound in air is 369 meters per second.

Substitute v=369 in the give equation.

`369=20√(273+t)`

Divide both sides by 20.

`(369)/(20)=√(273+t)`

`18.45=√(273+t)`

Taking square both the sides.

`(18.45)^2=273+t`

`340.4025=273+t`

Subtract 273 from both the sides.

`340.4025-273=t`

`67.4025=t`

`t\approx 67`

Therefore the velocity of sound in air is 369 meters per second at 67 degrees Celcius.