Sound waves and the doppler effect

In summary, the sound traveling from A to B takes the same amount of time to reach the observer on the ground at B, assuming that the plane has the same speed at both points. The jet's velocity at B is found to be 31.6 meters per second.
  • #1
seb26
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0

Homework Statement


A jet is flying horizontally from A to B. When the plane is directly overhead at B, a person on the ground (C) hears the sound coming from A. ABC is a right triangle in B. The angle BCA = 36 degrees.
The average temperature is 20 degrees Celsius. If the speed of the plane at A is 170 m/s, what is the speed at B, assuming that it has constant acceleration?

Homework Equations


f=1/T f: frequency; T: period
v= λ*f = λ/T λ: wavelength
fobserver= fplane*((v+vo)/(v+vp)) v=343m/s

The Attempt at a Solution


First off I don't see what steps to take to come up with the answer. There must some implicit data to take into consideration but I can't figure it out.
What I assume, since there is a right triangle with an angle given, is that one distance has to be found (AC) to find AB with sin.
I found the acceleration by taking t=1second. I know that the sound travels at 343m/s on AC and the speed the plane has after one second on AB is found by calculating vplane= sin(36)*343= 201.6m/s so the acceleration is a= (201.6-170)/1s= 31.6m/s2
I can't figure out how to get the distance from A to C or A to B.

PS: those values are given from my homework given by the teacher, on the book the same problem has 164m/s for the speed of the plane at A, same angle. The answer for the speed at B is 239m/s
 
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  • #2
Hi seb26, welcome to PF.
your relevant equations are irrelevant, because the problem is not based on Doppler effect.
It is just kinematic equation.
If vi is the initial velocity of the jet at A, vs is the velocity of the sound and t is the time taken by the jet to travel from A to B, then
AB = vi*t + 1/2*a*t^2 ...(1)
Sound starting form A takes the same time t to reach C. So
AC = vs*t...(2)
AB/AC = sinθ...(3) And vf - vi = at...(4)
Using above hints find the velocity of the jet at B.
 
Last edited:
  • #3
After a whole day of trying to crack this problem with my buddy, your advice is what led us to the answer. God bless you and those of you who help students like us out.

Peace,

Riaz
 

1. What are sound waves and how do they travel?

Sound waves are a type of mechanical wave that travels through a medium, such as air or water. These waves are produced by vibrations of an object, causing molecules in the medium to compress and expand, creating a wave-like pattern. The sound wave then travels through the medium until it reaches our ears, where it is detected as sound.

2. What is the doppler effect and how does it affect sound waves?

The doppler effect is the change in frequency or pitch of a sound wave when the source of the sound is in motion relative to the observer. This means that if the source of the sound is moving towards the observer, the frequency of the sound waves will increase, making the pitch higher. If the source is moving away, the frequency decreases and the pitch becomes lower.

3. How is the doppler effect used in everyday life?

The doppler effect has several practical applications in everyday life. It is used in radar technology to detect the speed and direction of moving objects, such as cars or airplanes. It is also used in medical imaging, such as ultrasounds, to measure blood flow and heart rate. The doppler effect is also used in music and sound production to create special effects and alter the perception of sound.

4. What factors can affect the doppler effect?

The doppler effect can be affected by several factors, including the speed and direction of the source and observer, the medium through which the sound is traveling, and the frequency of the sound waves. The speed of sound also plays a role in the doppler effect, as it determines how quickly the wave can travel through the medium.

5. Can the doppler effect occur with any type of wave?

The doppler effect can occur with any type of wave, not just sound waves. It can also be observed with light waves, where the color or frequency of light changes depending on the motion of the source and observer. This is known as the doppler shift and is used in astronomy to measure the speed and distance of stars and galaxies.

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