Question

A wave has a wavelength of 150 m and a velocity of 600 m/s. Using the equation in the question above, what would the frequency of the wave be?



How are frequency and wavelength related? If frequency increases, what happens to the wavelength of a wave?

Answer 1

To find the frequency of a wave, you can use the wave equation:

\[
v = f \lambda
\]

where:
- \( v \) is the velocity of the wave,
- \( f \) is the frequency,
- \( \lambda \) (lambda) is the wavelength.

From your question, you have:
- Wavelength (\( \lambda \)) = 150 m
- Velocity (\( v \)) = 600 m/s

Rearranging the equation to solve for frequency (\( f \)), you get:

\[
f = \frac{v}{\lambda}
\]

Now, substituting the values:

\[
f = \frac{600 \, \text{m/s}}{150 \, \text{m}} = 4 \, \text{Hz}
\]

So the frequency of the wave is **4 Hz**.

### Relationship between Frequency and Wavelength

Frequency and wavelength are inversely related in a wave. This means that if the frequency of a wave increases, the wavelength decreases, and vice versa.

Mathematically, this relationship can be summarized as:
- If \( f \) increases (more cycles per second), then \( \lambda \) (the distance between consecutive wave peaks) will decrease.
- If \( f \) decreases (fewer cycles per second), then \( \lambda \) will increase.

This inverse relationship is a direct consequence of the wave equation \( v = f \lambda \), where the speed of the wave (\( v \)) remains constant in a given medium.