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Question

The frequency of a radar is 780MHz.  The frequency of reflected wave from an airoplane is increased by 2.6kHz.  The velocity of the airoplane is 


A
2km/s
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B
1km/s
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C
0.5km/s
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D
0.25km/s
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Solution

The correct option is B 0.5km/s
Given : $$\delta=780\ MH{z}=780\times 10^{6}\ H{z}$$

$$\delta^{'}=2.6\times 780\times 10^{6}\ H{z}$$

$$v_{s}=0\ m/s$$

$$v=330 m/s$$

By Doppler effect formula

$$\delta^{'}=\delta\left ( \dfrac{v-v_{0}}{v-v_{3}} \right )$$

$$2.6\times 780\times 10^{6}=780\times 10^{6}\left ( \dfrac{330+v_{p}}{330-0} \right )$$

$$2.6\times 330=330+v_{p}$$

$$\Rightarrow v_{p}=330(1.6)$$

$$=500\ m/s$$

$$=0.5\ km/s$$

Physics

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