Question

Consider a tuning fork of frequency 256 Hz and an open organ pipe of slightly lower frequency. Both are at 17°C temperature. When sounded together, they produce 4 beats per second. When the temperature of air in the pipe is altered, the number of beats per second first diminishes to zero and then increases again to 4. Determine the quantum of temperature change in the pipe? Also, in what direction has the temperature of the air in the pipe been altered?

Answer 1

In an open organ pipe the frequency of the wave is n= V_t/λ where Vt 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

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

∴ Rise in temperature =35.7 – 17 = 18.7 °C.