If you increase the frequency of a sound wave four times, what will happen to its speed? A. The speed will increase four times.
В. The speed will decrease four times.
C. The speed will remain the same.
D. The speed will increase twice.
E. The speed will decrease twice.

B = - 33.89 dB

Explanation: The intensity of sound wave and square of distance from the source have an inverse relationship. This is given below as

Io/(r1)² = I/(r2)²

Where Io = intensity at a distance r1 away from source and I = intensity at a distance r2 away from the source.

For simplicity, we let our r1 = r in this question.

From the question, the farther listener is 49.5 times the distance of the closer listener away from the source.

That's if r1 =r then r2 = 49.5 ×r2.

By slotting this into the relationship above we have that

Io/r² = I/(49.5 ×r²)

Io/r² = I/(49.5)² × r².

We have that

Io×r² = I ×(49.5)² ×r²

r² cancels out on both sides of equation, we have that

Io = I(49.5)²

I/Io = I/(49.5)²

The sound intensity level is given as

B = 10 log ( I/Io)

But I/Io = I/(49.5)²

B = 10 log ( 1/(49.5)²)

B = 10 log ( 1/2450.25)

B = 10 × (-3.389)

B = - 33.89 dB