Question

A wave travels at a constant speed. How does the frequency change if the wavelength is reduced by a factor of 4?A.The frequency decreases by a factor of 16.B.The frequency decreases by a factor of 4.C.The frequency does not change.D.The frequency increases by a factor of 4.

Answer 1

To find:

Change in the frequency if the wavelength is reduced by a factor of 4.

Step-by-step explanation:

The speed of a wave is given by,

`v=f\lambda`

Where f is the frequency and λ is the wavelength of the wave.

If the wavelength is reduced by a factor of 4, then,

`\begin{gathered} v=f_n(\lambda)/(4) \\ \implies f\lambda=f_n(\lambda)/(4) \\ \implies f_n=4f \end{gathered}`

From above calculation, it is clear that the new frequency will be 4 times the old one.

Final answer:

Thus the correct answer is option D.