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Temka [501]
4 years ago
14

Two trains are traveling on the same track and in the same direction. The first train, which is behind the second train, blows a

horn whose frequency is 269 Hz. The second train detects a frequency of 290 Hz. If the speed of the second train is 13.7 m/s, what is the speed of the first train?
Physics
1 answer:
Andrews [41]4 years ago
5 0

Answer:

37.545 m/s

Explanation:

f' = Actual frequency of horn = 269 Hz

f = Observed frequency of horn = 290 Hz

v = Speed of sound in air = 343 m/s

v_0 = Speed of second train = 13.7 m/s

v_s = Speed of first train

From Doppler effect we have

f=f'\dfrac{v-v_0}{v-v_s}\\\Rightarrow v_s=v-\dfrac{f'}{f}(v-v_0)\\\Rightarrow v_s=343-\dfrac{269}{290}(343-13.7)\\\Rightarrow v_s=37.545\ m/s

The speed of the first train is 37.545 m/s

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The angle is  \phi =  0.45 0 ^o

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     The objective  focal length   f  =  1.33 \ m

     The  eyepiece focal length is  f_o =  2.82 \ cm  = 0.0282 \ m

      The diameter of the sunlight is  d  = 25000km =  2.5 *10^{7} \ m

       The distance of the sun from from the earth is  D =  1.5 *10^8 km  =  1.5 *10^{11} \ m

  Generally the magnification of the object is mathematically evaluated as

        m  =  -\frac{f_o }{f_e }

The negative  sign is because the lens of the telescope is  diverging light

 substituting values  

      m  =  -\frac{1.33 }{0.0282 }

      m  =  - 47.16 3

Now we can obtain the angle made by the object (sunlight ) with respect to the telescope  as follows  

        tan  \theta  = \frac{d}{D}

substituting values

      tan  \theta  = \frac{2.5 *10^{7}}{1.5*10^{11}}

      tan  \theta  =  0.0001667

      \theta=  tan^{-1}[0.0001667]

     \theta= 0.00955^o

The  magnification can  also be mathematically represented as

      m  =  \frac{\phi }{\theta }

Where \phi is the angle the image made with telescope

Since the negative sign indicate direction of light movement we will remove it from the calculation below

      =>   47.163  =  \frac{\phi}{0.00955}

     =>    \phi =  0.45 0 ^o

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3 years ago
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