Awoman stands a distance d from a loud motor that emits sound uniformly in all directions. the sound intensity at her position is an uncomfortable 3.9×10-3 w/m2. at a distance 3.8 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?

From the general equations of sound we know that the Intensity is directly proportional to the square of the distance. Therefore the relationship,

It will help us find the change between the two points. If the relationship is maintained, the intensity of point one versus point two will be given by the square of the distance of the other two points, therefore

From the statement it is given that the distance is 3.8, therefore

and

PART A) The intensity given under the previous equation found is

Therefore the sound intensity at point 2 is 0.00027W/m^2

PART B) For the sound level in decibels we will apply the logarithmic equation that relates the intensities, therefore

Where is the threshold intensity and is given by

Then,

Therefore the sound intensity level relative to the threshold of hearing is 84.31dB

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min