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The siren of a burglar alarm system has a frequency of 960Hz . During a patrol a security officer, traveling in his car , hears the siren of the alarm of a house and approaches the house at a constant velocity. A detector in his car registers the frequency of the sound as 1000 Hz . Calculate the speed at which the patrol car approaches the house . Use the speed of sound in air as 340m.s

Respuesta :

Answer:

14.2 m/s

Explanation:

When the source and receiver are getting closer, we can use the following equation:

[tex]f_o=(\frac{v+v_o}{v-v_s})f_s[/tex]

Where fo is the observed frequency, fs is the emitted frequency, vo is the speed of the observed, vs is the speed of the source, and v is the speed of the sound. Solving for vo, we get:

[tex]\begin{gathered} \frac{f_o}{f_s}=\frac{v+v_o}{v-v_s} \\ \\ \frac{f_o}{f_s}(v-v_s)=v+v_o \\ \\ \frac{f_o}{f_s}(v-v_s)-v=v_o \\ \\ v_o=\frac{f_o}{f_s}(v-v_s)-v \end{gathered}[/tex]

Then, replacing v = 340 m/s, vs = 0 m/s, fs = 960 Hz, and fo = 1000 Hz, we get:

[tex]\begin{gathered} v_r=\frac{1000}{960}(340-0)-340 \\ \\ v_r=14.2\text{ m/s} \end{gathered}[/tex]

Therefore, the speed of the patrol car is 14.2 m/s

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