Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

speed of sonar signal: v = 5470 km/h speed of detector: v D = 70 km/h speed of s

ID: 1724433 • Letter: S

Question

speed of sonar signal: v = 5470 km/h speed of detector: vD = 70 km/h speed of source: vs = 50 km/h Frequency of the sonar signal,f = 1000 Hz a)Frequency of the signal as detected by the U.s. subis, f ' = (v + vD) f / (v - vs)    = (1000 Hz)(5470 km/h + 70 km/h) / (5470km/h - 50km/h)   = 1022 Hz     = 1.022 kHz b)If the French sub were stationary, thefrequency of the reflected wave would be, fr =f(v+vD)/(v-vD) But since the French sub is movingtowards the reflected signal with speed vs isthen, fr' = fr(v+vs)/v    =f[(v+vs)(v+vD)/v(v-vD)] = 1.04x103Hz

Explanation / Answer

Given : .                 speedof sonar signal: v = 5470 km/h                speed of detector: vD = 70 km/h                speed of source: vs = 50 km/h                Frequency of the sonar signal,f = 1000 Hz . (a)    Form Doppler's effect : .                 Frequency of the signal detected is : .                        f ' = [ (v + vD) / (v - vs) ] *f   .                            = [ (5470 km/h + 70 km/h) / (5470 km/h - 50km/h) ] *(1000 Hz) .                             =  1.0221 * (1000 Hz)   .                             = 1.0221 kHz . (b)       The French sub ismoving towards the reflected signal with speed vs isthen, .                       fr' = fr ( v +vs) / v      --------------- (1) .             But the frequency of the reflected wave would be, .                        fr = f (v + vD) / ( v -vD)   . Substituting this value in equation (1) , we get .                        fr' =    { [ f (v +vD) / ( v - vD) ] * ( v +vs) } / v   .                             =    [ f (v + vD) * ( v + vs) ] / [ ( v - vD)* v ] .                             =    [ 1000 * (5470 + 70 ) * ( 5470 + 50 ) ] / [ (5470 - 70) * 5470 ] .                              =   1,035.3036    = 1.035 * 103   = 1.04 * 103    Hz . Hope this helps u! . Substituting this value in equation (1) , we get .                        fr' =    { [ f (v +vD) / ( v - vD) ] * ( v +vs) } / v   .                             =    [ f (v + vD) * ( v + vs) ] / [ ( v - vD)* v ] .                             =    [ 1000 * (5470 + 70 ) * ( 5470 + 50 ) ] / [ (5470 - 70) * 5470 ] .                              =   1,035.3036    = 1.035 * 103   = 1.04 * 103    Hz . Hope this helps u!