A wave travels at a speed of [tex][tex]$74 \, \text{m/s}$[/tex][/tex]. If the distance between crests is [tex][tex]$12 \, \text{m}$[/tex][/tex], what is the frequency of the wave? Use [tex][tex]$f = \frac{v}{\lambda}$[/tex][/tex].

A. [tex]6.2 \, \text{Hz}[/tex]
B. [tex]62 \, \text{Hz}[/tex]
C. [tex]0.16 \, \text{Hz}[/tex]
D. [tex]890 \, \text{Hz}[/tex]



Answer :

To find the frequency of a wave, we can use the formula:

[tex]\[ f = \frac{v}{\lambda} \][/tex]

where:
- [tex]\( f \)[/tex] is the frequency of the wave,
- [tex]\( v \)[/tex] is the speed of the wave, and
- [tex]\( \lambda \)[/tex] is the wavelength of the wave (the distance between crests).

Given:
- The speed [tex]\( v \)[/tex] of the wave is [tex]\( 74 \, \text{m/s} \)[/tex],
- The wavelength [tex]\( \lambda \)[/tex] is [tex]\( 12 \, \text{m} \)[/tex].

Plug these values into the formula:

[tex]\[ f = \frac{74 \, \text{m/s}}{12 \, \text{m}} \][/tex]

[tex]\[ f = 6.166666666666667 \, \text{Hz} \][/tex]

Rounding to one decimal place, the frequency [tex]\( f \)[/tex] is approximately [tex]\( 6.2 \, \text{Hz} \)[/tex].

So, the correct answer is:

A. [tex]\( 6.2 \, \text{Hz} \)[/tex]