Question

the ............. of sound produced by a vibrating string decrease with the increase in the length

Answer 1

PITCH..

Frequency of the tones of sound produced by a vibrating string decrease with increase in the length.  Pitch is related to frequency. As frequency increase the pitch increases.

Frequency is proportional to  v / (2L) ,
  v = speed of sound .    L = length of the string.

Answer 2

your required answer is pitch