# Human fingers are very sensitive, detecting vibrations with amplitudes as low as 2.4 X 10^-5 m. Consider a sound wave with a wavelength exactly 1000 times greater than the lowest amplitude detectable by fingers. The speed of sound in air is 377 m/s. What is this wave’s frequency?

Human fingers are very sensitive, detecting vibrations with amplitudes as low as $2.4×{10}^{-5}$ m. Consider a sound wave with a wavelength exactly 1000 times greater than the lowest amplitude detectable by fingers. The speed of sound in air is 377 m/s. What is this wave’s frequency?
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tiltat9h
Wavelength $=1000×$ Lowest amplitude
$\lambda =1000×2.4×{10}^{-5}m=2.4×{10}^{-2}m$
Speed, wavelength and frequency are related as
$v=f\lambda$
$f=\frac{v}{\lambda }=\frac{377m/s}{2.4×{10}^{-2}m}=15708.3Hz$