Question

A tuning fork of frequency 256 Hz and an open orange pipe of slightly lower frequency are at 170 C. When sounded together, they produce 4 beats per second. On altering the temperature of the air in the pipes, it is observed that the number of beats per second first diminishes to zero and then increases again to 4. By how much and in what direction has the temperature of the air in the pipe been altered?

Answer 1

In a open organ pipe the frequency of the wave is  n = V_t/λ where V_t is the velocity of wave at temperature t and λ=2L is the wavelength of the vibrating wave. If temperature of air inside the organ pipe changes, the velocity of wave also changes, since V ∝ √T.

n = V₁₇2I   where L = length of the pipe

Since beats decrease first and then increase to 4, the frequency of the pipe increases. This can happen only if the temperature increases. Let t be the final temperature, in Celsius,