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

A. wavelength [tex]$=$[/tex] frequency/speed
B. frequency [tex]$=$[/tex] wavelength/speed
C. wavelength [tex]$=$[/tex] speed/frequency
D. frequency [tex]$=$[/tex] speed [tex]$x$[/tex] wavelength


Sagot :

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.