A sound wave has a frequency of 704 Hz in air and a wavelength of 0.55 m. What is the temperature of the air? Relate the speed of sound in air to temper- ature in units of Kelvin, but answer in units of Celsius. Assume the velocity of sound at 0°C is 328 m/s. Answer in units of degC.

The speed of a wave (v) is equal to the frequency (f) times the wavelength (λ). The speed of sound in air is a function of the temperature (T):

v = 328 √(T / 273)

where v is in m/s and T is in Kelvin.

First, find the speed of the wave.

v = fλ

v = (704 Hz) (0.55 m)

v = 387.2 m/s

Next, find the temperature.

v = 328 √(T / 273)

387.2 = 328 √(T / 273)

T = 380 K

T = 107°C

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A sound wave has a frequency of 704 Hz in air and a wavelength of 0.55 m. What is the temperature of the air? Relate the speed of sound in air to temper- ature in units of Kelvin, but answer in units of Celsius. Assume the velocity of sound at 0°C is 328 m/s. Answer in units of degC.​

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A sound wave has a frequency of 704 Hz in air and a wavelength of 0.55 m. What is the temperature of the air? Relate the speed of sound in air to temper- ature in units of Kelvin, but answer in units of Celsius. Assume the velocity of sound at 0°C is 328 m/s. Answer in units of degC.