Neco 2024 Physics Question 27

At a temperature of \( 20^{\circ}\text{C} \) the speed of sound in air is given by \( v = 331 + 0.6T \) (m·s\( ^{-1} \)). A tube open at one end and closed at the other is made of brass with a linear expansion coefficient \( \alpha = 19\times10^{-6}\ \text{°C}^{-1} \). Its length at \( 20^{\circ}\text{C} \) is \( 0.500\) m. The temperature of the air inside the tube is raised uniformly to \( 30^{\circ}\text{C} \).\n\n(a) Determine the length of the tube at \( 30^{\circ}\text{C} \).\n\n(b) Calculate the fundamental frequency of the tube at \( 30^{\circ}\text{C} \).\n\n(c) A tuning fork of frequency \( 340\) Hz is sounded nearby. Find the beat frequency between the tuning fork and the tube's fundamental tone, to the nearest hertz.