If a wavelength is doubled and velocity remains the same, is the frequency halved? I say "yes".

If the velocity is halved and the wavelength remains the same, is the frequency halved. I say "yes" also.
Am I correct?

Yes.

frequency = V/(wavelength)

Thank you!

Yes, you are correct in both cases. Let me explain how to arrive at these answers.

To determine the relationship between wavelength, velocity, and frequency, we can use the equation:

c = λ * f

where:
c is the velocity of the wave (usually represented by the speed of light, approximately 3 × 10^8 meters per second),
λ is the wavelength, and
f is the frequency.

Let's consider each scenario separately:

1. If the wavelength is doubled while the velocity remains the same:
In this case, we let λ1 be the original wavelength and λ2 be the doubled wavelength. Since the velocity remains unchanged, we have to keep c constant. The equation becomes:

c = λ1 * f1 (Original equation)
c = λ2 * f2 (Doubling the wavelength)

Since c is the same in both equations, we can equate them:

λ1 * f1 = λ2 * f2

Since λ2 = 2 * λ1 (doubling the wavelength), we can substitute this into the equation:

λ1 * f1 = 2 * λ1 * f2

Simplifying:

f1 = 2 * f2

This proves that if the wavelength is doubled while the velocity remains the same, the frequency is indeed halved.

2. If the velocity is halved while the wavelength remains the same:
In this case, we let c1 be the original velocity and c2 be the halved velocity. The equation becomes:

c1 = λ * f1 (Original equation)
c2 = λ * f2 (Halved velocity)

Since the wavelength remains unchanged, we can equate the equations:

λ * f1 = λ * f2

Dividing through by λ:

f1 = f2

This proves that if the velocity is halved while the wavelength remains the same, the frequency remains the same as well.

So, your answers are indeed correct!