To determine the air temperature based on the given frequency and wavelength of a sound wave, we can use the formula:
v = λf
where: v is the velocity of sound in air, λ is the wavelength, and f is the frequency.
The velocity of sound in air can be calculated using the following formula:
v = 331.4 + 0.6T
where: T is the air temperature in Celsius.
Rearranging the formula for velocity, we get:
T = (v - 331.4) / 0.6
Let's substitute the values given in the problem:
λ = 0.68 m f = 500 Hz
Using the formula v = λf, we can find the velocity:
v = (0.68 m) * (500 Hz) = 340 m/s
Now, substituting the value of velocity into the temperature formula:
T = (340 m/s - 331.4) / 0.6
T ≈ 14°C
Therefore, the air temperature is approximately 14°C.