Answer:
The speed of sound in the atmosphere of Arrakis is 505.7 m/s.
Explanation:
given information:
male frequency, [tex]f_{m}[/tex] = 1180 Hz
female speed, [tex]v_{f}[/tex] = 30 m/s
female frequency, [tex]f_{f}[/tex] = 1250
to calculate the speed of sound in the atmosphere of Arrakis, we can use Doppler effect
[tex]f_{l} = \frac{v + v_{l} }{v+v_{s} } f_{s}[/tex]
where
[tex]f_{l}[/tex] = the frequency of listener
[tex]f_{s}[/tex] = the frequency of source
[tex]v[/tex] = speed of sound wave
[tex]v_{l}[/tex] = speed of listener
[tex]v_{s}[/tex] = speed of source
in this case, the male ornithoid is the source while the female is the listener.
[tex]v_{l}[/tex] or speed of listener is positive since the listener move toward the source, so
[tex]f_{l} = \frac{v + v_{l} }{v+v_{s} } f_{s}[/tex]
[tex]1250 = \frac{v +30}{v+0} 1180[/tex]
[tex]\frac{1250}{1180} = \frac{v+30}{v}[/tex]
[tex]\frac{125}{118} = \frac{v+30}{v}[/tex]
[tex]125v = 118v+3540[/tex]
[tex](125-118) v = 3540[/tex]
[tex]v = \frac{3540}{7}[/tex]
 = 505.7 m/s
