Question

Two ships in a heavy fog are blowing their horns, both of which produce sound with a frequency of 185.0 (see the figure ). One ship is at rest; the other moves on astraight line that passes through the one at rest.()If people on the stationary ship hear a beat frequency of 4.0 , what is the speed of the approaching ship?If people onthe stationary ship hear a beat frequency of 4.0 , what is the speed of the receding ship?

Answer 1

for approching ship f=c/(c-vs) *fo
f= 185+4 = 189

189 = c/(c-vs)*185
1-vs/c = 185/189 = .979
vs = .021c = .063*10^8m/s

for receding ship f=c/(c+vs) *fo
f= 185+4 = 189

181 = c/(c-vs)*185
1-vs/c = 181/189 = .958
vs = .042c = .127*10^8m/s

Answer 2