Calculating Plane Speed from Shockwave

[DmX0rZ]

1. Homework Statement

A plane passes from 900 meters over my head. I hear the shockwave after 2.2 seconds. At what speed in Mach is the plane flying ? Speed of sound = 331. 4 m/s

2. Homework Equations

Machs = speed of plane / speed of sound

3. The Attempt at a Solution

I don't have any clue where to go with this, maybe find the angle of the cone ? it gave me an angle of like .14 degrees and an impossible answer of the plane speed... dah

Thanks in advance

 

[Dick]

Call the mach ratio m. From this you know the horizontal distance the plane has traveled since it was overhead (in terms of m) since you know t=2.2sec. That let's you write down an expression for the cone angle in terms of the sides of the right triangle you just drew. You did draw it, right? Now you also know an expression for the angle of the mach cone in terms of m, I'm sure. Equate the two angles and solve for m.

 

[DmX0rZ]

do you mean tan(angle) = 2.2/900 ?

 

[DmX0rZ]

i made a drawing

 

[Dick]

do you mean tan(angle) = 2.2/900 ?

No. 2.2 has the dimensions of sec. 900 has dimensions of meters. The argument of tan is dimensionless. You want a ratio of velocities, tan(angle)=vs/(m*vs) where vs is the velocity of sound. Or just 1/m. Don't you have that written down someplace? I was wondering where you got 0.14 degrees.

 

[DmX0rZ]

nah we've been threw this section so fast, only thing i have is

vs = c / sin(angle)

and
machs = vs/c = 1 / sin(angle)where vs is velocity of thing moving, c is velocity of sound

 

[DmX0rZ]

How do i find the angle, that's the question :/

 

[Dick]

I don't know where that is coming from. Not surprising, since I haven't a clue as to what 'c' is supposed to mean. I think you may need a better reference than just your notes or you will just need to use physical common sense.

 

[DmX0rZ]

I mentionned in my post, c is the velocity of sound, in this problem we use c = 331.4

Plane is at 900 meters above my head and i hear the sound after 2.2 seconds, that's all i got.

 

[Dick]

How do i find the angle, that's the question :/

You need to write down two equations in the mach number m and solve them simultaneously. I wish I could hang around and help, but it's late here and I've got to go. Hopefully somebody else can pick this up.

 

[DmX0rZ]

thanks for the help !

 

[Dick]

I mentionned in my post, c is the velocity of sound, in this problem we use c = 331.4

Plane is at 900 meters above my head and i hear the sound after 2.2 seconds, that's all i got.

Ok. I don't think you mentioned that in your post. So vs is speed of the source? sin(angle) is not the right trig function. If vs=c then the cone angle should be 45 degrees. Write tan(angle) instead. Still got to go. Sorry.

 

[Dick]

Ok again, I feel guilty. tan(angle)=1/m. From the picture you drew, write down another expression for tan(angle) in terms of the sides of the geometric triangle. The hypotenuse distance is c*t. The vertical distance is 900m. What's another expression for tan(angle)?

 

[DmX0rZ]

HEY MAN, i think i finally got it:

first equation - nb of machs :

machs = velocity of plane / velocity of sound

second - distance ratio:

tan(angle) = x/900

third:

velocity of plane / velocity of sound = 1/sin(angle)

fourth:

x = velocity of plane * 2.2 secondes

x is the distance traveled by the plane
angle is the angle formed by the triangle of distances
machs is the nb of machs
and velocity of plane !

4 equations - 4 variables !


w00t

VELOCITY OF SOUND = 331.4

 

[DmX0rZ]

thanks anyway man.

youve been great !

good night :D

 

[Dick]

Maybe. I'm not quite following you. Zzzzz. You're welcome and good night to you.