Answer
The initial frequency of the trumpet is 445 Hz
Work Step by Step
The number of beats per second is the difference between the tuning fork's frequency of 440 Hz and the frequency played by the trumpet. Since there are initially 5 beats per second, the trumpet's initial frequency is either 435 Hz or 445 Hz.
After increasing the length, there are 3 beats per second. Thus the trumpet's frequency must be either 437 Hz or 443 Hz. Since increasing the length makes the frequency lower, the initial frequency of the trumpet must be 445 Hz.
