How are wavelength and frequency related?

Question

A.
If the distance between the crests of the waves increase, the frequency decreases.

B.
If the distance between the crests of the waves decrease, the frequency decreases.

C.
If the speed between the crests of the waves increases, the frequency increases.

D.
If the speed between the crests of the waves decreases, the frequency increases.

Answer 1

The relationship between wavelength and frequency is defined by the equation:

$$v=f\times \lambda$$

where:

• $v$ is the speed of the wave,
• $f$ is the frequency,
• $\lambda$ (lambda) is the wavelength.

From this relationship, we can derive that:

• If the wavelength ($\lambda$) increases, the frequency ($f$) decreases (assuming constant speed).
• If the wavelength decreases, the frequency increases (again assuming constant speed).

Now, let's look at your options:

A. If the distance between the crests of the waves increase, the frequency decreases.

• This is true, as an increase in wavelength leads to a decrease in frequency.

B. If the distance between the crests of the waves decrease, the frequency decreases.

• This is false; if the distance (wavelength) decreases, the frequency increases.

C. If the speed between the crests of the waves increases, the frequency increases.

• This is not necessarily true without context; if both speed and wavelength increase, frequency depends on the relationship.

D. If the speed between the crests of the waves decreases, the frequency increases.

• This is also not necessarily true; a decrease in speed can lead to a change in both wavelength and frequency depending on their relationship.

Therefore, the correct answer that accurately describes the relationship is A.