Which equation could be rearranged to calculate the frequency of a wave?

A. [tex]\text{wavelength} = \frac{\text{frequency}}{\text{speed}}[/tex]
B. [tex]\text{frequency} = \frac{\text{wavelength}}{\text{speed}}[/tex]
C. [tex]\text{wavelength} = \frac{\text{speed}}{\text{frequency}}[/tex]
D. [tex]\text{frequency} = \text{speed} \times \text{wavelength}[/tex]



Answer :

To determine which equations can be rearranged to solve for the frequency of a wave, let's analyze each equation step by step:

1. wavelength = frequency / speed

We need to solve for frequency:
[tex]\[ \text{wavelength} = \frac{\text{frequency}}{\text{speed}} \][/tex]
Multiply both sides by speed:
[tex]\[ \text{wavelength} \times \text{speed} = \text{frequency} \][/tex]
Therefore, this equation can be rearranged to calculate the frequency:
[tex]\[ \text{frequency} = \text{wavelength} \times \text{speed} \][/tex]

2. frequency = wavelength / speed

This equation is already solved for frequency, so no rearrangement is needed.

3. wavelength = speed / frequency

We need to solve for frequency:
[tex]\[ \text{wavelength} = \frac{\text{speed}}{\text{frequency}} \][/tex]
Multiply both sides by frequency:
[tex]\[ \text{wavelength} \times \text{frequency} = \text{speed} \][/tex]
Divide both sides by wavelength:
[tex]\[ \text{frequency} = \frac{\text{speed}}{\text{wavelength}} \][/tex]
Therefore, this equation can be rearranged to calculate the frequency:
[tex]\[ \text{frequency} = \frac{\text{speed}}{\text{wavelength}} \][/tex]

4. frequency = speed x wavelength

This equation is already solved for frequency, so no rearrangement is needed.

Given the analysis, the equations that can be rearranged to calculate the frequency of a wave are:

1. wavelength = frequency / speed
3. wavelength = speed / frequency

Thus, the correct equations that could be rearranged to calculate the frequency are given by the indices: [tex]\([1, 3]\)[/tex].