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# A police car horn emits a sound at a frequency $240\,Hz$ when the car is at rest. If the speed of the sound is $330\,m{\sec ^{ - 1}}$, the frequency heard by an observer who is approaching the car at a speed of $11\,m{\sec ^{ - 1}}$, is :A. $248\,Hz$B. $244\,Hz$C. $240\,Hz$D. $230\,Hz$

Last updated date: 23rd Feb 2024
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Hint:The Doppler effect, also known as the Doppler shift, describes the frequency shifts of any sound or light wave emitted by a moving object in relation to an observer. If an object approaches an observer, the waves it emits become compressed, resulting in a higher frequency.

${f_0} = \dfrac{{v + {v_0}}}{v}{f_s}$
Where, ${f_0}$= sound frequency of observer, $v$= sound wave speed, ${v_0}$= velocity of observer and ${f_s}$= actual frequency of sound wave.
${f_s} = 240\,Hz \\ \Rightarrow v = 330\,m{\sec ^{ - 1}} \\ \Rightarrow {v_0} = 11\,m{\sec ^{ - 1}} \\$
${f_0} = 240 \times \left( {\dfrac{{330 + 11}}{{330}}} \right) \\ \Rightarrow {f_0} = 240 \times \dfrac{{341}}{{330}} \\ \Rightarrow {f_0} = 8 \times {\dfrac{{{{341}}}}{{{{11}}}}^{31}} \\ \Rightarrow {f_0} = 8 \times 31 \\ \therefore {f_0} = 248\,Hz \\$