A SONAR system fixed in a submarine operates | vedclass

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(D) The operating frequency of the $SONAR$ is $f = 40.0 \; kHz = 40000 \; Hz$.Speed of the enemy submarine (observer),$v_o = 360 \; km/h = 360 	imes

Vedclass · Accepted Answer

$46$

Vedclass · Answer

(D) The operating frequency of the $SONAR$ is $f = 40.0 \; kHz = 40000 \; Hz$.Speed of the enemy submarine (observer),$v_o = 360 \; km/h = 360 	imes (5/18) \; m/s = 100 \; m/s$.Speed of sound in water,$v = 1450 \; m/s$.First,the enemy submarine acts as an observer moving towards the stationary $SONAR$ source. The frequency $f'$ received by the submarine is:$f' = f \left( \frac{v + v_o}{v} ight) = 40 \left( \frac{1450 + 100}{1450} ight) = 40 \left( \frac{1550}{1450} ight) \approx 42.76 \; kHz$.Next,the submarine acts as a source reflecting this frequency back to the $SONAR$. Since the submarine is moving towards the $SONAR$,the frequency $f''$ received by the $SONAR$ is:$f'' = f' \left( \frac{v}{v - v_o} ight) = 42.76 \left( \frac{1450}{1450 - 100} ight) = 42.76 \left( \frac{1450}{1350} ight) \approx 45.93 \; kHz$.Rounding to the nearest integer,the frequency is approximately $46 \; kHz$.

$A$ $SONAR$ system fixed in a submarine operates at a frequency of $40.0 \; kHz$. An enemy submarine moves towards the $SONAR$ with a speed of $360 \; km/h$. What is the frequency (in $kHz$) of sound reflected by the submarine (in $; kHz$)? Take the speed of sound in water to be $1450 \; m/s$.

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