**Do you enjoy going to the beach?**

During the summer, almost everyone enjoys going to the beach. They can swim, have picnics, and work on their tans. But if you get too much sun, you can burn. A particular set of solar wavelengths are especially harmful to the skin. This portion of the soar spectrum is known as UV B, with wavelengths of 280-320 nm. Sunscreens are effective in protecting the skin against both the immediate skin damage and the long-term possibility of skin cancer.

### Waves

Waves are characterized by their repetitive motion. Imagine a toy boat riding the waves in a wave pool. As the water wave passes under the boat, it moves up and down in a regular and repeated fashion. While the wave travels horizontally, the boat only travels vertically up and down. The **Figure** below shows two examples of waves.

A wave cycle consists of one complete wave – starting at the zero point, going up to a wave **crest**, going back down to a wave **trough**, and back to the zero point again. The **wavelength** of a wave is the distance between any two corresponding points on adjacent waves. It is easiest to visualize the wavelength of a wave as the distance from one wave crest to the next. In an equation, wavelength is represented by the Greek letter lambda \begin{align*}(\lambda)\end{align*}. Depending on the type of wave, wavelength can be measured in meters, centimeters, or nanometers (1 m = 10^{9} nm). The **frequency**, represented by the Greek letter nu \begin{align*}( \nu )\end{align*}, is the number of waves that pass a certain point in a specified amount of time. Typically, frequency is measured in units of cycles per second or waves per second. One wave per second is also called a Hertz (Hz) and in SI units is a reciprocal second (s^{-1}).

Figure B above shows an important relationship between the wavelength and frequency of a wave. The top wave clearly has a shorter wavelength than the second wave. However, if you picture yourself at a stationary point watching these waves pass by, more waves of the first kind would pass by in a given amount of time. Thus the frequency of the first waves is greater than that of the second waves. Wavelength and frequency are therefore inversely related. As the wavelength of a wave increases, its frequency decreases. The equation that relates the two is:

\begin{align*}\ c = \lambda \nu\end{align*}

The variable \begin{align*}c\end{align*} is the speed of light. For the relationship to hold mathematically, if the speed of light is used in m/s, the wavelength must be in meters and the frequency in Hertz.

#### Sample Problem: Wavelength and Frequency

The color orange within the visible light spectrum has a wavelength of about 620 nm. What is the frequency of orange light?

*Step 1: List the known quantities and plan the problem.*

Known

- wavelength \begin{align*}(\lambda)\end{align*} = 620 nm
- speed of light \begin{align*}(c)\end{align*} = 3.00 × 10
^{8}m/s - conversion factor 1 m = 10
^{9}nm

Unknown

- Frequency

Convert the wavelength to m, then apply the equation \begin{align*}c=\lambda\nu\end{align*} and solve for frequency. Dividing both sides of the equation by \begin{align*}\lambda\end{align*} yields:

\begin{align*}\nu=\frac{c}{\lambda}\end{align*}

*Step 2: Calculate.*

\begin{align*}620 \ \text{nm} \times \left(\frac{1 \ \text{m}}{10^9 \ \text{nm}}\right) &=6.20 \times 10^{-7} \ \text{m}\\ \nu = \frac{c}{\lambda}=\frac{3.0 \times 10^8 \ \text{m/s}}{6.20 \times 10^{-7} \ \text{m}} &=4.8 \times 10^{14} \ \text{Hz}\end{align*}

*Step 3: Think about your result.*

The value for the frequency falls within the range for visible light.

### Summary

- All waves can be defined in terms of their frequency and intensity.
- \begin{align*}c=\lambda\nu\end{align*} expresses the relationship between wavelength and frequency.

### Review

- Define wavelength.
- Define frequency.
- What is the relationship between wavelength and frequency?