## Related questions with answers

A sound source plays middle C (262 Hz). How fast would the source have to go to raise the pitch to C sharp (271 Hz)? Use 343 m/s as the speed of sound.

Solutions

VerifiedThis is a basic problem in which we use Doppler effect equation. Keep in mind that the stationary is detector and source is in motion. Which means that the $v_{d}=0$. Let's write the equation for Doppler effect:

$f_{d}=f_{s}\cdot \frac{(v-v_{d})}{(v-v_{s})}\tag1$

Where the $v$ is the speed of sound. In this problem $f_{d}$ is frequency of C sharp, while $f_{s}$ is the frequency of middle C.

$\color{#c34632}f_d = f_s\left(\dfrac{v-v_d}{v-v_s} \right)$

Substitute $v = 343$, $v_s=\text{Unknown}$, $v_d = 0$, $f_d = 271$ and $f_s = 262$

$271 = 262\left(\dfrac{343-0}{343-v_s} \right)$

Divide both sides by 262

$\dfrac{271}{262} = \dfrac{343}{343-v_s}$

Take reciprocal of both sides

$\dfrac{262}{271} = \dfrac{343-v_s}{343}$

$\dfrac{262}{271} = 1-\dfrac{v_s}{343}$

$\dfrac{v_s}{343}= 1-\dfrac{262}{271}$

Multiply both sides by 343

$v_s= 343\left[ 1-\dfrac{262}{271}\right]\approx11.39$

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