Question

Which statement correctly describes the relationship between frequency and wavelength?

As the frequency of a wave increases, the longer its wavelength is.
As the frequency of a wave increases, the shorter its wavelength is.
As the frequency of a wave increases, its wavelength remains the same.

Answer 1

The relationship between the frequency and wavelength of a wave is given by the equation:

v=λf, where v is the velocity of the wave, λ is the wavelength and f is the frequency. 

If we divide the equation by f we get:

λ=v/f

From here we see that the wavelength and frequency are inversely proportional. So as the frequency increases the wavelength decreases. 

So the second statement is true: As the frequency of a wave increases, the shorter the wavelength is.  

Answer 2

The wavelength and frequency are inversely proportional. So when frequency increases the wavelength decreases. Second statement is true.  

The relationship between the frequency and wavelength of a wave can best define by the equation:

v=λf

Where,

v -velocity of the wave

λ -wavelength

f -frequency.  

Divide the equation by f, we get:

$\bold {\lambda = \dfrac v{f}}$

From the equation, the wavelength and frequency are inversely proportional. So when frequency increases the wavelength decreases.  

Therefore, the second statement is true. when frequency increases the wavelength decreases.

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