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

Answer:

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

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

$f_{l} = \frac{v + v_{l} }{v+v_{s} } f_{s}$

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

$f_{l} = \frac{v + v_{l} }{v+v_{s} } f_{s}$

$1250 = \frac{v +30}{v+0} 1180$

$\frac{1250}{1180} = \frac{v+30}{v}$

$\frac{125}{118} = \frac{v+30}{v}$

$125v = 118v+3540$

$(125-118) v = 3540$

$v = \frac{3540}{7}$

  = 505.7 m/s

Answer 2

Answer:

775m/s

Explanation:

See attached file