Question

On the planet Arrakis, a male ornithoid sings at a frequency of 1180 Hz. When flying toward her mate at a speed of 30 m/s, a female ornithoid hears the sound at a frequency of 1250 Hz. What is the speed of sound in the atmosphere of Arrakis?

Answer 1

The speed of sound in the atmosphere of Arrakis is 505.7 m/s.

Step-by-step explanation:

given information:

male frequency,
`f_(m)` = 1180 Hz

female speed,
`v_(f)` = 30 m/s

female frequency,
`f_(f)` = 1250

to calculate the speed of sound in the atmosphere of Arrakis, we can use Doppler effect

`f_(l) = (v + v_(l) )/(v+v_(s) ) f_(s)`

where

`f_(l)` = the frequency of listener

`f_(s)` = the frequency of source

`v` = speed of sound wave

`v_(l)` = speed of listener

`v_(s)` = speed of source

in this case, the male ornithoid is the source while the female is the listener.

`v_(l)` or speed of listener is positive since the listener move toward the source, so

`f_(l) = (v + v_(l) )/(v+v_(s) ) f_(s)`

`1250 = (v +30)/(v+0) 1180`

`(1250)/(1180) = (v+30)/(v)`

`(125)/(118) = (v+30)/(v)`

`125v = 118v+3540`

`(125-118) v = 3540`

`v = (3540)/(7)`

= 505.7 m/s

Answer 2

775m/s

Step-by-step explanation:

See attached file