To determine which of the given equations can be rearranged to calculate the frequency of a wave, let's analyze each one step-by-step.
1. Equation: wavelength = frequency / speed
To solve for frequency:
[tex]\[
\text{frequency} = \text{wavelength} \times \text{speed}
\][/tex]
2. Equation: frequency = wavelength / speed
This equation is already given in terms of frequency. There’s no need to rearrange it.
3. Equation: wavelength = speed / frequency
To solve for frequency:
[tex]\[
\text{frequency} = \text{speed} / \text{wavelength}
\][/tex]
4. Equation: frequency = speed x wavelength
This equation is already given in terms of frequency. There’s no need to rearrange it.
Analyzing the results:
- The first equation was rearranged to: [tex]\( \text{frequency} = \text{wavelength} \times \text{speed} \)[/tex]
- The second equation: [tex]\( \text{frequency} = \text{wavelength} / \text{speed} \)[/tex]
- The third equation was rearranged to: [tex]\( \text{frequency} = \text{speed} / \text{wavelength} \)[/tex]
- The fourth equation: [tex]\( \text{frequency} = \text{speed} \times \text{wavelength} \)[/tex]
Among these, equation two, "frequency = wavelength / speed," is already in a form that directly calculates the frequency without needing rearrangement.
Thus, the correct equation that can be used directly to calculate the frequency of a wave is:
[tex]\[
\text{frequency} = \text{wavelength} / \text{speed}
\][/tex]
The corresponding index of this equation in the provided list is 1.
