[Guest]

Inspiered by this earlier topic

A supersonic jet is flying at 400m/s from a long way away at an altitude of 1km. Given that the jet flies directly above you how close will it be (horizontally) before you hear it?

Assume: speed of sound is 330 m/s, there is no wind and you can hear sound form a long way off.

[Guest]

never........i"m deaf!!!

[Guest]

The plane could be right above you but you'd be hearing the sound from when it was roughly 3.5 to 4 secs away

[Guest]

Inspiered by this earlier topic

A supersonic jet is flying at 400m/s from a long way away at an altitude of 1km. Given that the jet flies directly above you how close will it be (horizontally) before you hear it?

Assume: speed of sound is 330 m/s, there is no wind and you can hear sound form a long way off.

assuming you wouldnt hear the aircraft coming as it was travelling faster than the sound it was producing, then you would hear it first once it had passed directly overhead and travelled a further 1212m. However most supersonic flight would be taking place around 10000m height above sea level-therefore by scaling the result of the previous answer by a factor of 10 then a real supersonic aircraft at 30000 feet+ would pass overhead and travel a further 12.12km before it became audible.

[bonanova]

The plane could be right above you but you'd be hearing the sound from when it was roughly 3.5 to 4 secs away

You'd hear it after it passed overhead.

The sonic boom is a cone which trails the plane, like the wake of a boat in water.

The angle of the cone [from vertical] is arc tan[vplane/vsound] = arctan[40/33].

Project back to where it hits the ground and divide that horizontal distance by 400.

[Guest]

im confused its traveling faster then sound so wouldn't the closest sound to you be the sound that it makes right above u. so its just the time it take the sound to reach from the distance it is above you

it would take 1km/.330km/s to reach you or 3.03030303 seconds so it would be 3.0303s*400m/s away or 1212.1212m ive never studied sonic booms tho so i might be working on false assumptions

as i said ive never studied it but i dont think the sound actually travels in a cone it just looks like one because as the sound travels down there is more traveling down in front of it since the jet is faster then sound. So it makes a cone shape but well i guess thats the same thing, i dont know, anybody know if im right / where i went wrong.

[Glycereine]

im confused its traveling faster then sound so wouldn't the closest sound to you be the sound that it makes right above u. so its just the time it take the sound to reach from the distance it is above you

it would take 1km/.330km/s to reach you or 3.03030303 seconds so it would be 3.0303s*400m/s away or 1212.1212m ive never studied sonic booms tho so i might be working on false assumptions

as i said ive never studied it but i dont think the sound actually travels in a cone it just looks like one because as the sound travels down there is more traveling down in front of it since the jet is faster then sound. So it makes a cone shape but well i guess thats the same thing, i dont know, anybody know if im right / where i went wrong.

Yes

[Guest]

im confused its traveling faster then sound so wouldn't the closest sound to you be the sound that it makes right above u. so its just the time it take the sound to reach from the distance it is above you

it would take 1km/.330km/s to reach you or 3.03030303 seconds so it would be 3.0303s*400m/s away or 1212.1212m ive never studied sonic booms tho so i might be working on false assumptions

as i said ive never studied it but i dont think the sound actually travels in a cone it just looks like one because as the sound travels down there is more traveling down in front of it since the jet is faster then sound. So it makes a cone shape but well i guess thats the same thing, i dont know, anybody know if im right / where i went wrong.

You can look here if you want.

[Guest]

You can look here if you want.

Basic trig fun 3.03s, and now and I will remember tan(@) = 1/M for a long long time to come

[Guest]

The first sound of plane that reachs you will be the one when the plane was 4 seconds away from directly overhead.. see attached image below for the math where T=0 means the time when plane is directly overhead

It reaches after 1.718 seconds and the corresponding horizontal distance is 687 m

Edited June 15, 2009 by DeeGee

[Guest]

The first sound of plane that reachs you will be the one when the plane was 4 seconds away from directly overhead.. see attached image below for the math where T=0 means the time when plane is directly overhead

It reaches after 1.718 seconds and the corresponding horizontal distance is 687 m

Well I haven't studied enough physics to know about this cone thing people are mentioning but I agree with this post. You can find the exact answer using calculus.

t = time, d = horizontal distance. speed of jet = 400m/s, speed of sound = 330m/s, height = 1000m).

So let’s form an equation of the time it takes for the sound to reach you at a distance d including the time it takes for the jet to reach this distance.

t = d/400 + sqrt(1000^2 + d^2)/330

dt/dd = 1/400 + 2d/(660 * sqrt(1000^2 + d^2)) = 0

sqrt(1000^2 + d^2) = -800d/660

1000^2 + d^2 = d^2 * 1600/1089

d = -1459.834052m

I checked the graph to make sure that it is definitely negative 1459 not the positive root. So this is where the jet will be when it produced the first sound wave you will hear.

It takes sound sqrt(1000^2 + 1459.834^2)/330 seconds to reach you form here. That’s 5.36s.

The jet will have travelled a further 5.36 * 400 m in this time which means that you will hear the sound when it has passed over you and is now 685m away.

[Guest]

so hears my theory revised. The plane is moveing faster so the sound it produces when above you will be the closest sound horizonatally. What i forgot is the sound is moving directly towards you where the plane isnt so it will happen when

400/cos(angle from plane to you)<333

or the component of the planes velocity that is moving directly toward you is less then the component of sound that is moving directly toward you (all of it) or a 33.6435 angle so this sound will be coming from a

so if it is 1 km in the air then it is 1/tan(theta) away from you or 1.502639 km

and the sound takes 1502.639/333 or 4.51243 s

in which the jet has traveled 1804.97 meters subtract the distance it was from you

1.80497-1.502639=.30233 km

i thought something was wrong with my previous answer i think this is right tho

[Guest]

it keeps telling me ive used all my attachment space so this is just to fix that maybe

[Guest]

ok think i figured out the attachments here is a better explantation

notice in the picture you are changing where the right angle is and which side is the hypot but not changing the angle we're using

after you look at the picture read this it made the file too big to attach

notice that if we use the point that sound overruns(is faster towards you than) the plane as our starting point it would take 1502.639/400=3.7565s for the plane to be above you and then another 1000/333=3.003 for the sound to reach you or 6.7565 total. this is obviously 2ish seconds worse so my old answer (first answer not the last one) was wrong

Edited June 16, 2009 by final

[Guest]

hey im just wondering (or maybe my ego is) is this right or wrong... because i think it is different from everyone elses answer. and as it is smaller if all my math is right this is the right (or at least closer) answer and i cant find a math mistake

i dont know if i stated my answer outside the attachment (it was easier then words) but my answer is 302.33 m or (302.33/400)=.755825 seconds from when it passed

the other number of seconds that is listed in my solution is the time the sound takes to reach you from the time the closest sound is released. also i think my math (or diagrams) would work perfectly for if you are traveling at the speed of sound you would hear it when it is exactly over you.

[Guest]

wow actually relooked at my work instead of just bumpin the feed and found the mistake got to love doing math in your head. That way when you write it down you already have your mistakes ingrained in your mind.