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a female vocalist with a soprano voice can sing as high as 1000 hz. given that the speed of sound is 345 m/s what is the wavelength if the sound waves

Respuesta :

0.345 m.

Explanation

The wavelength is the distance that the wave travels in each cycle. The wave travels 345 meters in each second. Let the wavelength of this wave be [tex]\lambda[/tex]. That's the distance the wave travels in one cycle.

The frequency of the sound wave is 1 000 Hz, meaning that there are 1 000 cycles in each second. The wave travels a distance of 1 000 wavelengths in one second. That would be a distance of [tex]1,000\;\lambda[/tex].

From the speed of the wave, the wave travels 345 meters in one second. In other words,

[tex]1,000\;\lambda = 345[/tex].

[tex]\lambda = \dfrac{345}{1,000} = 0.345\;\text{m}[/tex].

To generalize:

[tex]\lambda = \dfrac{v}{f}[/tex],

where

  • [tex]\lambda[/tex] wavelength of the wave,
  • [tex]v[/tex] the speed of the wave, and
  • [tex]f[/tex] the frequency of the wave.
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