8.5.1 Doppler Effect Problem

[wilco.civi1055]

No matter how hard I try I can not solve this doppler problem from the book: 8.5.1 Doppler Effect Problem (SI units) vs = - 262(331 + 0)/277 + 331 = 17.9 m/s. I broke down the equation and could not get this answer. Can someone help me understand how to break fo = fs(V + vo )/(V - vs) into the final equation.

[mcat_premed3832]

fo = fs(V + vo )/(V - vs)

Multiply both sides by (V-vs):

fo(V - vs) = fs(V + vo )

Divide both sides by fo

V - vs = fs(V + vo )/fo

Subtract "V" from both sides

-vs = fs(V + vo )/fo - V

Multiply through by -1

vs = -fs(V + vo )/fo + V

Now plug in and use the sign conventions described in the problem:

fo = observed frequency = 277

fs = source frequency = 262

V = velocity of the sound wave =

vo = observer velocity = 0 (observers are not moving)

vs = source velocity = unknown

[wilco.civi1055]

thank you, now when i work out the problem the answer that i am getting is not what the book has.

[mcat_premed3832]

vs = -fs(V + vo )/fo + V

vs = -262 (331 + 0)/277 + 331

vs = 331 - 262 (331)/277 {note: 331/277 = approx 1.195}

vs = 331 - 262 (1.195) {note: 262 (1.195) = 313.1}

vs = 331 - 313.1

vs = 17.9 m/s