Finding the Distance Between Sound and Wave Maxima at a Train Station

In summary, the question is asking to find the distance between the zero and first order maxima as a function of time. Both trains are approaching the station at an initial velocity of 120 km/h and slowing down to a halt in 20 seconds. They are also whistling at 5000 Hz. The solution involves considering the doppler effect and using the equations f = fo [c/c-v], λ = c/f, and v = 120/3.6 m/s. The given solution at t=0 is 893/60000 m, but the correct answer is 893/30000 m. This is because the waves from the two trains interfere constructively at a distance of ##{1\over
  • #1
timetraveller123
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Homework Statement


Two trains approach the train station from opposite sides each moving at an initialvelocity of 120 km/h with respect to the station and slowing down to a halt in 20seconds. If both trains are whistling at 5000 Hz, find the distance between the zeroand first order maxima as a function of time.
4-e89aee99f1.jpg


so this is the question:
when they say zero and first order maxima they mean it only lies on the x-axis right meaning the zero order maxima is at the centre of the two trains and the first order maxima is at distance d away where the extra length traveled is exactly a wavelength so i did the question just for the part when the trains are not decelerating ie t=0 and my solution does not match the given one please help or is the first order maxima in the y direction

Homework Equations


f = fo [c/c-v] --- doppler effect for train approaching
c= 331m/s
λ = c/f
v = 120/3.6 m/s
the given solution is at t =0 the distance between the zero and first order is 893/60000 m

The Attempt at a Solution


the first order is offset to one side by distance d so
2d is the extra length traveled the sound wave coming from the other side hence
2d=λ
2d = c/f
2d = c(c-v)/(2c fo)
plugging in gets me 893/30000 which is twice of correct answer please help
 
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  • #2
vishnu 73 said:
2d is the extra length traveled the sound wave coming from the other side
True, but doesn't the one from the opposite side travel over a little less distance ?
 
  • #3
BvU said:
True, but doesn't the one from the opposite side travel over a little less distance ?
i am sorry i don't get what you mean could please explain your point thanks
 
  • #4
Make a drawing and you'll see it more easily. Constructive interference occurs where one wave travels ##{1\over 2}\lambda ## further and the other ##{1\over 2}\lambda ## less.
 
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  • #5
BvU said:
Make a drawing and you'll see it more easily. Constructive interference occurs where one wave travels ##{1\over 2}\lambda ## further and the other ##{1\over 2}\lambda ## less.
oh i see it now thanks so much !
 
  • #6
You're welcome :smile:
 
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  • #7
no wait sir i did what you said and all of a sudden i am confused again as i once again get d =λ/2 please enlighten me as if one wave were to travel 1/2λ lesser it implies that that is d
 
  • #8
BvU said:
Make a drawing and you'll see it more easily. Constructive interference occurs where one wave travels ##{1\over 2}\lambda## further and the other ##{1\over 2}\lambda## less.
I made the drawing and find I have to correct myself: not ##{1\over 2}\lambda## but ##{1\over 4}\lambda## ... o:)

Can you see why ?

(It's astounding to see how much more instructive an animated picture is wrt one on paper ! How wonderful all these newfangled technologies o0) )
 
  • #9
thank you sir i figured out my mistake i was all along using cos graph for both side only to realize that when the two cos graphs collide they will super pose to zero at every point i should have used cos graph on one side and -cos graph on the other side and then your 1/4λ thing works thanks for your troubles really appreciate it !
 

Related to Finding the Distance Between Sound and Wave Maxima at a Train Station

1. What is sound interference?

Sound interference refers to the interaction of sound waves from two or more sources. When sound waves overlap, they can either cancel each other out or combine to create a new sound wave with a different amplitude or frequency.

2. What causes sound interference?

Sound interference is caused by the superposition of sound waves. This occurs when two or more waves meet and their amplitudes add together. Depending on the phase relationship between the waves, the resulting sound can either be louder or quieter than the individual waves.

3. How does wave interference affect sound quality?

Wave interference can greatly affect the quality of sound. Constructive interference, where waves combine to increase the amplitude, can create louder and clearer sound. Destructive interference, where waves cancel each other out, can result in weaker and distorted sound.

4. What are the two types of interference in sound waves?

The two types of interference in sound waves are constructive interference and destructive interference. Constructive interference occurs when two waves with the same frequency and amplitude meet, resulting in a louder sound. Destructive interference occurs when two waves with opposite phases meet, resulting in a weaker or cancelled out sound.

5. How can sound interference be controlled or minimized?

Sound interference can be controlled by adjusting the amplitude, frequency, and phase of sound waves. In some cases, using sound-absorbing materials or positioning sound sources strategically can also help minimize interference. Advanced technologies such as active noise cancellation also use sound interference principles to reduce unwanted noise.

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