Chapter 2: Q58E (page 66)

To catch speeders, a police radar gun detects the beat frequency between the signal it emits and that which reflects off a moving vehicle. What would be the beat frequency for an emitted signal of 900 Mhz reflected from a car moving at 30 m/s ?

Short Answer

Expert verified

The beat frequency between the Doppler shifted frequency and original frequency is $180 Hz$ .

Step by step solution

Write the given data from the question

The speed of the car, $v_{s} = 30 m / s$

The frequency of the emitted signal, f=900Mhz

Beat frequency

The expression for the Doppler shift is given as follows.

$\frac{∆ f}{f} = \frac{v_{5}}{c}$

Here, $v_{5}$ is the speed of the source, c is the speed of the light and $∆ f$ is the beat frequency.

Calculate the beat frequency for the emitted signal

To calculate the beat frequency, equation for beat frequency and Doppler shift required.

$\frac{∆ f}{f} = \frac{2 V_{t a r g e t}}{c}$ …… (i)

Calculate the beat frequency,

Substitute $3 \times 10^{8} m / s for c, 900 MHz for f and 30 m / s for V_{s}$ into equation (i).

$\frac{∆ f}{900 \times 10^{6}} = \frac{2 \times 30}{3 \times 10^{8}} ∆ f = \frac{60}{3 \times 10^{8}} \times 900 \times 10^{6} ∆ f = \frac{540}{3} ∆ f = 180 H z$

Hence the beat frequency between the Doppler shifted frequency and original frequency is 180 Hz .

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To catch speeders, a police radar gun detects the beat frequency between the signal it emits and that which reflects off a moving vehicle. What would be the beat frequency for an emitted signal of 900 Mhz reflected from a car moving at 30 m/s ?

Short Answer

Step by step solution

Write the given data from the question

Beat frequency

Calculate the beat frequency for the emitted signal

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