Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. On the planet Arrakis a male ornithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 Hz. If the stationary female hears a tone of 1240 Hz, what is the speed of sound in the atmosphere of Arrakis?

Solution 43E The speed of the male ornithoid is 25 m/s. His frequency of singing is 1200 Hz. The stationary female mate of him heard a frequency of 1240 Hz. Here we can use doppler effect, by the equation, V s fO= (1 + V ) s ---------------------(1) Where f is the frequency received by the observer at rest. O V is the velocity of the source. s V is the velocity of sound waves in the planet. fsis the frequency of the source So, according to equation (1), 1240 = (1 + 25) × 1200 V 25 1 + V = 1240 / 1200 = 1.033 25 / V = 1.033 1 = 0.033 V = 25 / 0.033 = 757.57 m/s = 758 m/s (approximately) Conclusion: So, the speed of sound in Arrakis planet is 758 m/s.