Final answer:
To find the length of a tube that resonates at 128 Hz when the air temperature is 45.0 °C, calculate the speed of sound at that temperature and use the relationship between speed, frequency, and wavelength for a tube closed at one end.
Step-by-step explanation:
In order to find the length of a tube closed at one end that resonates at a fundamental frequency of 128 Hz when air temperature is 45.0 °C, we can use the relationship between the speed of sound, the frequency, and the wavelength for the first harmonic in such a tube. The speed of sound depends on air temperature and can be calculated using the formula v = (331.4 + 0.6*T) m/s, where T is the temperature in °C. On a day when the temperature is 45.0 °C, the speed of sound v is v = (331.4 + 0.6*45) m/s.
For a tube closed at one end, the length L is ⅔ (one-fourth) of the wavelength λ of the fundamental frequency. Since λ = v/f, where f is the frequency, we can find L by the formula L = λ/4 = v/(4*f). Substituting in the values for v (calculated before) and f (128 Hz), the length L of the tube can be calculated for the specified conditions.