An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = $324 m s^{- 1}$ .

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Solution

Let the speed of the car =x m/sec

So, Freqency heard at car n,

$= \frac{v + v_{c a r}}{v} \times n_{0} = \frac{324 + x}{324} \times 400$

and frequency heard by opeartor for reflected sound wave

$n_{1} = \frac{324}{324 - x} \times n$

$\Rightarrow 410 = \frac{324}{324 - x} \times \frac{324 + x}{324} \times 400$

$\Rightarrow 324 (410 - 400) = 810 x \Rightarrow x = 4 m / s e c$

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An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = 324ms−1.

Let the speed of the car =x m/sec So, Freqency heard at car n, =v+vcarv×n0=324+x324×400 and frequency heard by opeartor for reflected sound wave n1=324324−x×n ⇒410=324324−x×324+x324×400 ⇒324(410−400)=810x⇒x=4m/sec

An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = $324 m s^{- 1}$ .