Question #cef58

1 Answer
Jun 13, 2017

#4 * 10^(-4)# #"m"#

Explanation:

The idea here is that wavelength and frequency have an inverse relationship that depends on the speed of the wave

#color(blue)(ul(color(black)(lamda * nu = v)))#

Here

  • #lamda# is the wavelength of the wave
  • #nu# is its frequency
  • #v# is the speed of the wave

In your case, you know that the generator produces #50# pulses per second. Since frequency is simply a measure of the number of events per unit of time, you can say that the waves generated have a frequency of

#nu = "50 pulses"/"1 s" = "50 s"^(-1)#

Rearrange the equation to solve for #lamda#

#lamda * nu = v implies lamda = v/(nu)#

and plug in your values to find

#lamda = ("2.0 cm" color(red)(cancel(color(black)("s"^(-1)))))/(50color(red)(cancel(color(black)("s"^(-1))))) = "0.04 cm"#

If you want, you can convert this to meters by using the fact that

#"1 m" = 10^2# #"cm"#

to get

#color(darkgreen)(ul(color(black)(lamda = 4 * 10^(-4)color(white)(.)"m")))#

The answer is rounded to one significant figure.