Question

On the planet Arrakis a male ornithoid is flying toward his mate at $\mathbf{25}\mathbf{m}/\mathbf{s}$while singing at a frequency of $\mathbf{1200}\mathbf{Hz}$. If the stationary female hears a tone of $\mathbf{1240}\mathbf{Hz}$, what is the speed of sound in the atmosphere of Arrakis?

Short answer

Sound travels at a speed of $775\text{\hspace{0.17em}m}/\text{s}$.

Step-by-step solution

Given data

Speed of the male ornithoid is $\mathbf{2}5\mathbf{m}/\mathbf{s}$

Frequency while singing by male is$1200\text{\hspace{0.17em}\hspace{0.17em}Hz}$

Frequency heard by the female is $1240\text{\hspace{0.17em}\hspace{0.17em}Hz}$

Doppler’s effect

The Doppler’s effect is given by the formula,

${\mathbf{f}}_L\mathbf{=}\frac{\mathbf{v}\mathbf{+}{\mathbf{v}}_L}{\mathbf{v}\mathbf{+}{\mathbf{v}}_S}{\mathbf{f}}_S$

where

• role="math" localid="1655813921062" ${\mathit{f}}_{\mathbf{L}}$is the frequency of the wave that is heard by the listener.
• $\mathit{v}$is the wave speed.
• ${\mathit{v}}_{\mathbf{L}}$is the listener’s speed.
• ${\mathit{v}}_{\mathbf{s}}$is the sound source’s speed.
• ${\mathbf{f}}_{\mathbf{s}}$is the sound source’s frequency.

Consider the male is moving towards the listener

So, the speed of the sound in the atmosphere is $775\text{\hspace{0.17em}m/s}$.