A submarine (A) travelling at 18, km/hr is be | vedclass

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(B) Given:Speed of sound in water,$V = 1500\, m/s$Speed of submarine $A$,$V_A = 18\, km/hr = 18 	imes \frac{5}{18} = 5\, m/s$Speed of submarine $B$,$

Vedclass · Accepted Answer

$502$

Vedclass · Answer

(B) Given:Speed of sound in water,$V = 1500\, m/s$Speed of submarine $A$,$V_A = 18\, km/hr = 18 	imes \frac{5}{18} = 5\, m/s$Speed of submarine $B$,$V_B = 27\, km/hr = 27 	imes \frac{5}{18} = 7.5\, m/s$Source frequency,$f_0 = 500\, Hz$Step $1$: Frequency received by submarine $A$ (acting as an observer):$f' = f_0 \left( \frac{V - V_A}{V - V_B} ight) = 500 \left( \frac{1500 - 5}{1500 - 7.5} ight)$Step $2$: Submarine $A$ reflects this sound,acting as a source,and submarine $B$ receives it (acting as an observer):$v = f'' = f' \left( \frac{V + V_B}{V + V_A} ight)$Substituting $f'$:$v = 500 \left( \frac{1500 - 5}{1500 - 7.5} ight) \left( \frac{1500 + 7.5}{1500 + 5} ight)$$v = 500 \left( \frac{1495}{1492.5} ight) \left( \frac{1507.5}{1505} ight)$$v \approx 500 	imes 1.001675 	imes 1.001661 \approx 501.67\, Hz$Rounding to the nearest integer,$v \approx 502\, Hz$.

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