Waves and sounds, finding the speed of a jet using the speed of sound

In summary, a person on the ground hears the sound coming from a jet flying horizontally at point B while it is directly overhead. Given that the average temperature of the air is 20 oC and the speed of the plane at point A is 180 m/s, the question asks for the speed of the plane at point B assuming constant acceleration. Using kinematic equations and trigonometry, the distance between points A and B can be found, and with the given information, the speed of the plane at point B can be calculated.
  • #1
atriancarlos
1
0

Homework Statement



A jet is flying horizontally, as the drawing shows. When the plane is directly overhead at B, a person on the ground hears the sound coming from A in the drawing. The average temperature of the air is 20 oC. If the speed of the plane at A is 180 m/s, what is its speed at B, assuming that it has a constant acceleration?

http://edugen.wileyplus.com/edugen/courses/crs2216/art/qb/qu/c16/ch16p_101.gif


Homework Equations


x=1/2(Vo+V)t
V=λ/Period (T)= λ x Frequency
c (speed of sound)= 343 m/s at 20 degrees celsius
T (period)= 2 ∏/ω(angular frequency)

The Attempt at a Solution



first I tried to use the kinematic equation to find the distance between the points A and B but I am stuck because i need the time in order to find the distance (x) between the two points. I think I need to use the pythagorean theorem because the angle made by point B is 90 degrees and I am giving the angle of the observer on the ground as 36 degrees, meaning that the last angle should be 54 degrees to add up to 180 degrees. Do I need to use the law of cosines or sines since I know three angles? any help is appreciated
 

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  • #2
Can't view your picture.
 
  • #3
In your image, the right triangle has sides (using your formula), (v_0 + v)*t/2 , h, c*t.

The length (v_0 + v)*t/2 is related to the length c*t using some trig. t will cancel.

This is late, hope it helps.
 

What is the relationship between waves and sounds?

Waves are the physical phenomenon that carries sound. Sound is a type of wave that travels through a medium, such as air or water, and is created by vibrations or disturbances.

What is the speed of sound?

The speed of sound is approximately 343 meters per second in dry air at room temperature.

How can the speed of a jet be determined using the speed of sound?

The speed of a jet can be determined by measuring the time it takes for a sound wave to travel from the jet to a fixed point and back. This can be done using specialized equipment, such as a radar gun or a sonic boom tracker.

Why is it important to know the speed of a jet?

Knowing the speed of a jet is important for various reasons, including flight safety, air traffic control, and aircraft performance analysis.

Are there any factors that can affect the speed of sound?

Yes, the speed of sound can be affected by temperature, humidity, and altitude. As temperature increases, the speed of sound also increases, while humidity and altitude can decrease the speed of sound.

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