Question

Question #cef58

Answer 1

`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.