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Chapter 2: Q45E (page 541)

On the planet Arrakis a male ornithoid is flying toward his mate at 25鈥�m/swhile singing at a frequency of 1200鈥夆赌�Hz. If the stationary female hears a tone of 1240鈥夆赌�Hz, what is the speed of sound in the atmosphere of Arrakis?

Short Answer

Expert verified

Sound travels at a speed of 775鈥尘/s.

Step by step solution

01

Given data

Speed of the male ornithoid is 25鈥夆赌�m/s

Frequency while singing by male is1200鈥夆赌塇z

Frequency heard by the female is 1240鈥夆赌塇z

02

Doppler’s effect

The Doppler鈥檚 effect is given by the formula,

fL=v+vLv+vSfS

where

  • role="math" localid="1655813921062" fLis the frequency of the wave that is heard by the listener.
  • vis the wave speed.
  • vLis the listener鈥檚 speed.
  • vsis the sound source鈥檚 speed.
  • fsis the sound source鈥檚 frequency.
03

Consider the male is moving towards the listener

fL=v+vLv+vSfS1240鈥塇锄=v+0v鈭�25鈥尘/s脳1200鈥塇锄vv鈭�25鈥尘/s=3130v=775鈥尘/s

So, the speed of the sound in the atmosphere is 775鈥尘/s.

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