A motor cycle starts from rest and accelerates along a straight path at 2 m /s2. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest?

( Speed of sound = 330 ms -1)

  • Option 1)

    49\: m

  • Option 2)

    98\: m

  • Option 3)

    147\: m

  • Option 4)

    196\: m    

 

Answers (1)

As we learnt in

frequency of sound when source is moving towards the observer and observer is moving away from source -

\nu {}'= \nu _{0}.\frac{C-V_{0}}{C-V_{\Delta }}

- wherein

C= Speed of sound

V_{0}= Speed of observer

V_{\Delta }= speed of source

\nu _{0 }= Original frequency

\nu {}'= apparent frequency

 

 Suppose the moter cycle has travelled a distance S if velocity at that point V=\sqrt{2aS}

\upsilon'=\left(\frac{330-v}{330} \right )\upsilon=0.94=\frac{330-v}{330}

V=19.8\ ms^{-1}

\therefore\ \; S=\frac{V^{2}}{2a}=\frac{(19.8)^{2}}{2\times 2}

    S = 98 mt

Correct option is 2.

 


Option 1)

49\: m

This is an incorrect option.

Option 2)

98\: m

This is the correct option.

Option 3)

147\: m

This is an incorrect option.

Option 4)

196\: m    

This is an incorrect option.

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