The air column in a pipe closed at one end is made to vibrate in its second overtone by tuning fork of frequency 440Hz The speed of sound in air is 330 m/s. End corrections may be neglected. Let P0 denote the mean pressure at any point in the pipe, and ΔP0 the maximum amplitude of pressure variation.
1. Find the length L of the air column.
2. What is the amplitude of pressure variation at the middle of the column?
3. What are the maximum and minimum pressures at the open end of the pipe?
4. What are the maximum and minimum pressures at the closed end of the pipe?
5. A solid body X of heat capacity C is kept in a an atmosphere whose temperature is TA = 300 K. At time t = 0, the temperature of X is T0 = 400 K. It cools according to Newton’s law of cooling. At time t1 its temperature is found to be 350 K.
At this time (t1) the body X is connected to a large body Y at atmospheric temperature TA through a conducting rod of length L, cross-sectional area A and thermal conductivity K. The heat capacity of Y is so large that any variation in its temperature may be neglected. The cross-sectional area A of the connecting rod is small compared to the surface area of X. Find the temperature of X at time t = 3t1.
Source: 1998 JEE