Calculate the longest wavelength of sound that a human can hear. The speed of sound in air is 340m/s?

1 Answer
Nam D.
Jun 16, 2018

#17# meters

Explanation:

I assume here that the frequency that most humans can hear range from #20 \ "Hz"# to #20000 \ "Hz"#.

Wavelength is given by the equation:

#lambda=v/f#

where:

  • #lambda# is the wavelength is meters

  • #v# is the velocity in meters per second

  • #f# is the frequency in hertz

From here, we see that wavelength is inversely proportional to frequency, and so to get the maximum wavelength, we need to have the smallest frequency that's hearable, which is #20 \ "Hz"#.

So, we get:

#lambda=(340 \ "m/s")/(20 \ "Hz")#

#=(340"m"color(red)cancelcolor(black)("s"^-1))/(20color(red)cancelcolor(black)("s"^-1)) \ (because 1 \ "Hz"=1 \ "s"^-1)#

#=17 \ "m"#

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