Crave The Wave B

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Mon Apr 27, 2015 9:23 pm

Correct. Your turn (whoever it is that I should be addressing)!
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

Scioly99
Member
Member
Posts: 34
Joined: Fri Feb 28, 2014 9:48 pm
Division: B
State: TX
Contact:

Re: Crave The Wave B

Postby Scioly99 » Mon Apr 27, 2015 10:46 pm

A jet plane flies at a constant altitude of 700m above ground. An observer on the ground hears a sonic boom 6 seconds after the plane passes directly overhead. what is the speed of the plane? (assume that the velocity of sound in air is constant at all altitudes)

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Tue Apr 28, 2015 1:34 am

I've studied sonic booms before, but I don't know how to do this one... Is it...

ANS
1065.16m/s
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

Scioly99
Member
Member
Posts: 34
Joined: Fri Feb 28, 2014 9:48 pm
Division: B
State: TX
Contact:

Re: Crave The Wave B

Postby Scioly99 » Tue Apr 28, 2015 2:08 am

i Think that's right

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Wed Apr 29, 2015 12:10 am

In retrospect, the question is unsolvable... Try it but replace the 6s with just 1s and see how what you get compares to mine.
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

User avatar
UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 726
Joined: Sun Jan 18, 2015 3:42 pm
Division: C
State: PA
Location: (0, 0)
Contact:

Re: Crave The Wave B

Postby UTF-8 U+6211 U+662F » Wed Apr 29, 2015 12:18 am

RontgensWallaby wrote:In retrospect, the question is unsolvable... Try it but replace the 6s with just 1s and see how what you get compares to mine.

That's why I didn't reply.

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Wed Apr 29, 2015 10:21 pm

Anyone going to solve the problem where 6 seconds is replaced by 1 second?
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Thu Apr 30, 2015 9:09 pm

RontgensWallaby wrote:Anyone going to solve the problem where 6 seconds is replaced by 1 second?


As no one seems to be answering the question, I'll just put that the answer is 393.474 m/s.
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

User avatar
UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 726
Joined: Sun Jan 18, 2015 3:42 pm
Division: C
State: PA
Location: (0, 0)
Contact:

Re: Crave The Wave B

Postby UTF-8 U+6211 U+662F » Thu Apr 30, 2015 9:52 pm

RontgensWallaby wrote:
RontgensWallaby wrote:Anyone going to solve the problem where 6 seconds is replaced by 1 second?


As no one seems to be answering the question, I'll just put that the answer is 393.474 m/s.

???

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Fri May 01, 2015 1:26 am

Here's how you'd do it. Because the observer hears the sound after the plane passes by him, the plane has already broken the sound barrier and thus the sound is propagating backwards from it in the shape of a cone. (If you don't understand this there are plenty of online tutorials). For this problem, we'll make a simple diagram of when the observer first hears the sound. A cross-section of the sound cone is a triangle, which for simplicity's sake we will divide into a right triangle, as we can ignore the top half of the sound cone. The link below shows a picture of the right triangle we will use, where point A is the location of the observer, point B is the location of the plane, side a is the path taken by the plane, and side c is the edge of the sound cone (remember, this is the exact point where the sound reaches the observer). Because the plane constantly travels 700m above the ground, the length of side b is 700m. And since the observer hears the sound 1s after the plane passes directly overhead, side a is 1s multiplied by the velocity, which we'll refer to as x; therefore, side a is x. Now, angle B is what's called the Mach angle, and it has a special property. The sine of the Mach angle is equal to the speed of sound divided by the velocity of the plane. Therefore, we can create a similar right triangle (with the same Mach angle); however, in this triangle, side b is 343 (the speed of sound) and side c is x (the velocity of the plane). Because the side length ratio of our first triangle to our second triangle is 700/343, or about 2.041, side c in our first triangle is equal to 700x/343. Applying the Pythagorean Theorem to this first triangle, who has side a as x, side b as 700m, and side c as 700x/343, we can find that x=393.474m/s.





http://www.montereyinstitute.org/course ... age107.gif
Ignore the 30 deg mark at angle B, and the side labeled "4" will be referred to as side "b".
Last edited by RontgensWallaby on Fri May 01, 2015 1:34 am, edited 1 time in total.
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Fri May 01, 2015 1:34 am

OK. Someone else please post another question
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

User avatar
UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 726
Joined: Sun Jan 18, 2015 3:42 pm
Division: C
State: PA
Location: (0, 0)
Contact:

Re: Crave The Wave B

Postby UTF-8 U+6211 U+662F » Fri May 01, 2015 1:41 am

RontgensWallaby wrote:Here's how you'd do it. Because the observer hears the sound after the plane passes by him, the plane has already broken the sound barrier and thus the sound is propagating backwards from it in the shape of a cone. (If you don't understand this there are plenty of online tutorials). For this problem, we'll make a simple diagram of when the observer first hears the sound. A cross-section of the sound cone is a triangle, which for simplicity's sake we will divide into a right triangle, as we can ignore the top half of the sound cone. The link below shows a picture of the right triangle we will use, where point A is the location of the observer, point B is the location of the plane, side a is the path taken by the plane, and side c is the edge of the sound cone (remember, this is the exact point where the sound reaches the observer). Because the plane constantly travels 700m above the ground, the length of side b is 700m. And since the observer hears the sound 1s after the plane passes directly overhead, side a is 1s multiplied by the velocity, which we'll refer to as x; therefore, side a is x. Now, angle B is what's called the Mach angle, and it has a special property. The sine of the Mach angle is equal to the speed of sound divided by the velocity of the plane. Therefore, we can create a similar right triangle (with the same Mach angle); however, in this triangle, side b is 343 (the speed of sound) and side c is x (the velocity of the plane). Because the side length ratio of our first triangle to our second triangle is 700/343, or about 2.041, side c in our first triangle is equal to 700x/343. Applying the Pythagorean Theorem to this first triangle, who has side a as x, side b as 700m, and side c as 700x/343, we can find that x=393.474m/s.





http://www.montereyinstitute.org/course ... age107.gif
Ignore the 30 deg mark at angle B, and the side labeled "4" will be referred to as side "b".

Okay. I'll ask a question:
A sound wave of 8 dB travels 1 m. What is the volume of the attenuated sound wave?

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Fri May 01, 2015 1:52 am

Again, not sure if this is right.
If it's wrong, I'd appreciate if you sent me a link about it.

ANS
7.385 dB
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr

User avatar
UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 726
Joined: Sun Jan 18, 2015 3:42 pm
Division: C
State: PA
Location: (0, 0)
Contact:

Re: Crave The Wave B

Postby UTF-8 U+6211 U+662F » Fri May 01, 2015 7:24 pm

Oops, um, said that wrong. :oops:
A sound wave of 8 dB travels 1 meter and ends up being 5 dB. What is the volume of the attenuated sound wave after 1.5 meters?

RontgensWallaby
Member
Member
Posts: 58
Joined: Wed Apr 15, 2015 12:00 am
Division: C
State: GA
Location: Small Magellanic Cloud (my messages may be a couple of years late)
Contact:

Re: Crave The Wave B

Postby RontgensWallaby » Sat May 02, 2015 4:49 pm

UTF-8 U+6211 U+662F wrote:Oops, um, said that wrong. :oops:
A sound wave of 8 dB travels 1 meter and ends up being 5 dB. What is the volume of the attenuated sound wave after 1.5 meters?


Oh, ok.

ANS
1.6375 dB
Every great and deep difficulty bears in itself its own solution. It forces us to change our thinking in order to find it. - Niels Bohr


Return to “2015 Question Marathons”

Who is online

Users browsing this forum: No registered users and 1 guest