Question

Problem 2: Sound generators We have identical sound generators at the same place generating sound waves. Half of the generators are in phase and the other half has random phases. The total intensity is 20 times bigger than the intensity of a single generator. How many sound generators do we have in total? iii) 12 (iv) 16 (v) 20

Answer 1

Let the number of sound generators be x and the intensity of a single generator be I.

Since half of the generators are in phase the total intensity due to all of them is  $(x/2)^{2}I=x^{2}I/4$.

The total intensity due to the remaining generators which have random phase =$xI/2$.

Now we have $x^{2}I/4+xI/2=20I$ i.e the expression for total intensity due to all the generators.

i.e.$x^{2}/4+x/2-20=0$ i.e. $x^{2}+2x-80=0$ .

On solving the above quadratic equation we obtain x=8.

Thus the total number of sound generators is 8.

The correct option is ii).