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

Click For Summary
SUMMARY

The discussion focuses on calculating the speed of a jet at point B using the speed of sound and kinematic equations. The speed of sound at 20°C is established as 343 m/s. The jet's speed at point A is given as 180 m/s, and the problem involves determining the speed at point B while considering constant acceleration. The use of trigonometric principles, specifically the Pythagorean theorem and possibly the law of sines or cosines, is suggested to solve for the distance and time between points A and B.

PREREQUISITES
  • Understanding of kinematic equations, specifically x = 1/2(Vo + V)t
  • Knowledge of the speed of sound, c = 343 m/s at 20°C
  • Familiarity with trigonometric principles, including the Pythagorean theorem
  • Basic concepts of angular frequency and period in wave mechanics
NEXT STEPS
  • Study the application of kinematic equations in projectile motion
  • Learn how to apply the law of sines and cosines in triangle problems
  • Explore the relationship between sound speed and temperature variations
  • Investigate the effects of acceleration on the motion of objects
USEFUL FOR

Students in physics or engineering courses, educators teaching kinematics and wave mechanics, and anyone interested in the practical applications of sound speed in aviation contexts.

atriancarlos
Messages
1
Reaction score
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
 

Attachments

  • ch16p_101.gif
    ch16p_101.gif
    1.3 KB · Views: 755
Last edited:
Physics news on Phys.org
Can't view your picture.
 
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.
 

Similar threads

Sound Wave Interference and Finding the Path Differences with Diagrams
  • · Replies 20 ·
Replies
20
Views
5K
I Need to Calculate the Speed of Sound for a Lab
  • · Replies 4 ·
Replies
4
Views
3K
What is the speed of sound and time period of oscillating particles?
  • · Replies 5 ·
Replies
5
Views
3K
Frequency of Reflected Underwater Sound Wave
  • · Replies 2 ·
Replies
2
Views
2K
How Can the Speed of Sound Help Determine Room Temperature?
  • · Replies 3 ·
Replies
3
Views
3K
Speed of Sound using a Resonant tube
  • · Replies 12 ·
Replies
12
Views
4K
Depth of a well (using speed of sound)
  • · Replies 6 ·
Replies
6
Views
3K
Sound Wave Problem: Frequency of Note in Amphitheater
  • · Replies 6 ·
Replies
6
Views
7K
Sound wave Interference from Two Speakers
  • · Replies 3 ·
Replies
3
Views
4K
Determining the speed of sound in air
  • · Replies 1 ·
Replies
1
Views
1K