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While you watch a parade, a band on a float passes you. You detect the frequency of a note played on a flute to be 356 Hz when the float is coming toward you and 348 Hz after the float passes you. Part A At what speed is the float traveling

Respuesta :

Answer:

Float is travelling at speed of 3.86 m/s

Explanation:

As per Doppler's effect we know that when source and observer moves relative to each other then the frequency is different from actual frequency

so here when source moves closer to the observer

[tex]f_1 = f_o(\frac{v}{v - v_s})[/tex]

now we have

[tex]356 = f_o(\frac{v}{v - v_s})[/tex]

again when source moves away from the observer then we have

[tex]f_2 = f_o(\frac{v}{v + v_s})[/tex]

[tex]348 = f_o(\frac{v}{v + v_s})[/tex]

now divide above two equations

[tex]\frac{356}{348} = \frac{v + v_s}{v - v_s}[/tex]

[tex]1.023 = \frac{v + v_s}{v - v_s}[/tex]

[tex]1.023( v - v_s) = (v + v_s)[/tex]

here we know that the speed of sound in air is 340 m/s

so we have

[tex]1.023(340 - v_s) = (340 + v_s)[/tex]

[tex]7.816 = 2.023 v_s[/tex]

now we have

[tex]v_s = 3.86 m/s[/tex]

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