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A whistle of frequency 589 Hz moves in a circle of radius 54.6 cm at an angular speed of 16.1 rad/s. What are (a) the lowest and (b) the highest frequencies heard by a listener a long distance away, at rest with respect to the center of the circle? (Take the speed of sound in air to be 343 m/s.)

Respuesta :

Answer:

[tex]f_{min} = 574.3 Hz[/tex]

[tex]f_{max} = 604.5 Hz[/tex]

Explanation:

As per Doppler's effect of sound we know that when source and observer moves relative to each other then the frequency of sound observed by the observer is different from real frequency of sound.

As the source is moving here in this case so the frequency is given as

[tex]f = f_o\frac{v}{v\pm v_s}[/tex]

part a)

for lowest frequency we will have

[tex]f_{min} = 589(\frac{343}{343 + R\omega})[/tex]

here we know that

R = 54.6 cm

[tex]\omega = 16.1 rad/s[/tex]

now we have

[tex]f_{min} = 589(\frac{343}{343 + 0.546(16.1)})[/tex]

[tex]f_{min} = 574.3 Hz[/tex]

part b)

for maximum frequency we will have

[tex]f_{max} = 589(\frac{343}{343 - R\omega})[/tex]

here we know that

R = 54.6 cm

[tex]\omega = 16.1 rad/s[/tex]

now we have

[tex]f_{max} = 589(\frac{343}{343 - 0.546(16.1)})[/tex]

[tex]f_{max} = 604.5 Hz[/tex]

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