How Far Must a Helicopter Fly to Decrease Sound Intensity by a Factor of 4?

[bbfcfm2000]

I am confused about a homework problem and was hoping that maybe somebody here can help...

Homework Problem
When a helicopter is hovering 1090 m directly overhead, an observer on the ground measures a sound intensity I. Assume that sound is radiated uniformly from the helicopter and that ground reflections are negligible. How far (in m) must the helicopter fly in a straight line parallel to the ground before the observer measures a sound intensity of I/4?

According to my textbook, "If the distance increases by a factor of two, the sound intensity decreases by a factor of 2^2=4"

So I figured that to find the answer I simply muiltiply the initial distance (1090m) by 2 so the sound intensity (I) decreases by 4 (I/4). When I do the math, my answer is 2180m but this is not the correct answer.

What might I be doing wrong?

Thanks in advance!

 

[learningphysics]

I am confused about a homework problem and was hoping that maybe somebody here can help...

Homework Problem
When a helicopter is hovering 1090 m directly overhead, an observer on the ground measures a sound intensity I. Assume that sound is radiated uniformly from the helicopter and that ground reflections are negligible. How far (in m) must the helicopter fly in a straight line parallel to the ground before the observer measures a sound intensity of I/4?

According to my textbook, "If the distance increases by a factor of two, the sound intensity decreases by a factor of 2^2=4"

So I figured that to find the answer I simply muiltiply the initial distance (1090m) by 2 so the sound intensity (I) decreases by 4 (I/4). When I do the math, my answer is 2180m but this is not the correct answer.

What might I be doing wrong?

Thanks in advance!

You have to use the pythagorean theorem. 2180m is the distance from the helicopter to the observer. But the question asks how far the helicopter flew horizontally. Draw a sketch...

 

[bbfcfm2000]

Thank you for the help!

Ah ha, I see. Now my problem then becomes a basic algebra issue. I understand that the pythagorean theorem is A^2 + B^2 = C^2 and when I sub in the values I get as an equation:

C^2=sqrt(A^2 + B^2) --> 2180^2 = sqrt(1090^2 + B^2)

But I do not know how to solve for B^2 when A and C are both known. Can someone maybe help with my algebra on this one?

I added a graphic to this thread that depicts the problem.

Thanks again!

 

[dextercioby]

No,no,your formula expressing Pythagora's theorem is completely wrong

$$2180^{2}=1090^{2}+B^{2}$$

Solve for "B",knowing that only a positive solution si acceptable...

Daniel.

 

[learningphysics]

Thank you for the help!

Ah ha, I see. Now my problem then becomes a basic algebra issue. I understand that the pythagorean theorem is A^2 + B^2 = C^2 and when I sub in the values I get as an equation:

C^2=sqrt(A^2 + B^2) --> 2180^2 = sqrt(1090^2 + B^2)

you inserted a wrong sqrt here. It should be:

C^2=A^2 + B^2 --> 2180^2 = 1090^2 + B^2

Solve for B here.

 

[bbfcfm2000]

Thanks for all the replies, I got it! I really did know how to do this (solve for B^2 that is), I must have just had a mental block as my brain has been on vacation for a month.

1887.94 m.

Thanks again!