An oscillator vibrating at 1270 Hz produces a sound wave that travels through an ideal gas at 325 m/s when the gas temperature is 22.0 ∘C. For a certain experiment, you need to have the same oscillator produce sound of wavelength 28.5 cm in this gas What should the gas temperature be to achieve this wavelength?

     T = 53.44 ° C

Explanation:

For this exercise we will use the relationship between the speed of sound and the wavelength and frequency

          v = λ f

          v = 0.285 1270

          v = 361.95 m / s

The speed of sound is related to temperature in degrees Celsius

          v = 331 √(1 + T / 273)

          v² / 331² = 1 + T / 273

          T / 273 = v² / 331² -1

            T = 273 (v² / 331² -1)

Let's calculate

        T = 273 (361.95²/331² -1)

        T = 53.44 ° C