The speed of sound waves in air at 300K is 332 m/s. At what temperature will the speed be 574 m/s?
To find the temperature at which the speed of sound waves in air will be 574 m/s, we can make use of the relationship between the speed of sound and temperature known as the formula for the speed of sound:
v = 331.4 * √(T/273.15)
where:
- v is the speed of sound in meters per second
- T is the temperature in Kelvin
We start with the initial speed of sound and temperature given:
v1 = 332 m/s
T1 = 300 K
Next, we will solve for the unknown temperature using the equation and the given value for the final speed of sound:
v2 = 574 m/s
Rearranging the formula, we have:
v1/v2 = √(T1/T2)
Squaring both sides of the equation, we get:
(v1/v2)^2 = T1/T2
Plugging in the values, we have:
(332/574)^2 = 300/T2
Calculating (332/574)^2, we find:
(0.578)^2 = 300/T2
Simplifying further, we obtain:
0.334 = 300/T2
Now, let's isolate T2 by multiplying both sides of the equation by T2:
0.334 * T2 = 300
Dividing both sides of the equation by 0.334, we find:
T2 = 300 / 0.334
Evaluating 300 / 0.334, we get:
T2 ≈ 897 K
So, the temperature at which the speed of sound waves in air will be 574 m/s is approximately 897 Kelvin.