Question

p.8.6 formative 1
the diagram below shows a wave with its wavelength indicated in red.
what will happen to the waves frequency if its wavelength is made twice as long?
it will go to zero.
it will stay the same.
it will double.
it will decrease.

Explanation:

Step1: Recall the wave equation

The wave equation is \(v = f\lambda\), where \(v\) is the wave speed, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step2: Assume wave speed is constant

In many common cases (e.g., light in a vacuum, sound in a given medium), the wave speed \(v\) is constant. So, \(f=\frac{v}{\lambda}\).

Step3: Analyze when \(\lambda\) doubles

If \(\lambda_{new} = 2\lambda_{old}\), then \(f_{new}=\frac{v}{\lambda_{new}}=\frac{v}{2\lambda_{old}}\). Since \(f_{old}=\frac{v}{\lambda_{old}}\), we have \(f_{new}=\frac{1}{2}f_{old}\).

Answer:

It will decrease.