Here's how to understand the relationship between velocity, frequency, and wavelength, and how they change together:

The Fundamental Relationship

The key equation is:

* v = fλ

where:

* v is the velocity (or speed) of the wave

* f is the frequency of the wave

* λ is the wavelength of the wave

What Happens When Velocity and Frequency Are Halved

If both velocity (v) and frequency (f) are reduced to one half, the wavelength (λ) will remain the same. Here's why:

1. Start with the original equation: v = fλ

2. Halve the velocity and frequency: (v/2) = (f/2)λ

3. Simplify: v = fλ

Notice that the "2" cancels out on both sides of the equation, leaving the original relationship unchanged.

In Conclusion

When you reduce both the velocity and frequency of a wave by half, the wavelength remains constant.