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A student standing in a canyon yells "echo", and her voice produces a sound wave of frequency of f = 0.61 kHz. The echo takes t = 3.9 s to return to the student. Assume the speed of sound through the atmosphere at this location is v = 322 m/s.

Respuesta :

Answer:

[tex]d=627.9\ m[/tex]  is the distance from the obstacle of reflection.

wavelength [tex]\lamb=0.5279\ m [/tex]

Explanation:

Given that:

  • frequency of sound, [tex]f=610\ Hz[/tex]
  • time taken for the echo to be heard, [tex]t=3.9\ s[/tex]
  • speed of sound, [tex]v=322\ m.s^{-1}[/tex]

We know,

[tex]\rm distance = speed \times time[/tex]

During an echo the sound travels the same distance back and forth.

[tex]2d=v.t[/tex]

[tex]2d=322\times 3.9[/tex]

[tex]d=627.9\ m[/tex]  is the distance from the obstacle of reflection.

Now the wavelength of sound waves:

[tex]\lambda=\frac{v}{f}[/tex]

[tex]\lambda=\frac{322}{610}[/tex]

[tex]\lamb=0.5279\ m [/tex]

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