College

A wave is traveling through a medium. The velocity can be calculated using the equation [tex]v = f \times \lambda[/tex].

What is the velocity of a wave that has a frequency of [tex]30,000 \, \text{Hz}[/tex] and a wavelength of [tex]5.0 \, \text{m}[/tex]?

A. [tex]150,000 \, \text{Hz}[/tex]

B. [tex]150,000 \, \text{m/s}[/tex]

C. [tex]6,000 \, \text{Hz}[/tex]

Answer :

To find the velocity of a wave, we use the formula:

[tex]\[ v = f \times \lambda \][/tex]

where:
- [tex]\( v \)[/tex] is the velocity of the wave,
- [tex]\( f \)[/tex] is the frequency of the wave,
- [tex]\( \lambda \)[/tex] (lambda) is the wavelength of the wave.

In this problem, you are given:
- The frequency [tex]\( f = 30,000 \)[/tex] Hz
- The wavelength [tex]\( \lambda = 5.0 \)[/tex] meters

Let's plug these values into the formula:

[tex]\[ v = 30,000 \, \text{Hz} \times 5.0 \, \text{m} \][/tex]

When you perform the multiplication:

[tex]\[ v = 150,000 \, \text{m/s} \][/tex]

Thus, the velocity of the wave is [tex]\( 150,000 \text{ m/s} \)[/tex]. This matches the second option: [tex]\( 150,000 \text{ m/s} \)[/tex].