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A sonar system fixed in a submarine operates at a frequency 40.0 kHz, An enemy subarine moves towords the sonar with a speed of 360 km/h. What is the frequency of sound refielcted by the submarine? (Take the speed of sound in water to be 1450 m/s)

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Answer Text

52.3 KHz45.93 KHz c.62.49 Kz54.34 kHz

Answer :
B
Solution :
Sonar frequency, <br> `" "v_(s)=40KHz=40xx10^(3)Hz` <br> Speed of enemy submarine, <br> `v_(s)=360Km//h = 360xx 5/18m//s=100m//s(therefore1m//h=5/18m//s)` <br> Speed of sound in water = 1450 m/s <br> Apparent frequency received by the energy submarine, <br> `v'=((v+v_(o))/(v))v=((1450+100)/(1450))xx40xx10^(3)` <br> `" "=42.76xx10^(3)Hz` <br> Now, the reflected waves received by sonar having a different frequency <br> `" "((v)/(v-v_(s)))v'` <br> Here `v_(s)`=100 m/s is velocity of enemy submarine. <br> `therefore" "v'=((1450)/(1450-100))xx42.76xx10^(3)` <br> `" "=45.93xx10^(3)Hz` <br> `" "=45.93kHz`

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