Scientific Understanding

**What sections should I know before attempting to learn this section?**

**How do you calculate the wavelength or frequency of light?**

In addition to the wavelength and frequency being related to the color of light, they are also related to each other. If you have a LONG wavelength then the frequency is LOW and if you have a SHORT wavelength then the frequency is HIGH. This relationship is also demonstrated in the equation below.

Wavelength * (Frequency) = speed

λ (f) = speed

The equation above is the general way to calculate the speed of a wave. However, the equation below is usually the one you see in a chemistry class. It is more specific to calculating the frequency and wavelength of the speed of light but all the concepts behind it are the same. Wavelength (λ) is measured in the units of meters (m). Frequency (f) is measured in the units of Hertz (Hz). The speed of light (c) is a constant number and its value is 3.0 * 10^{8} m/s.

Wavelength * (Frequency) = speed of light

λ (f) = c

**VIDEO Speed of light, Frequency, and Wavelength Calculation Demonstrated Example 1****:** If the frequency of the light is 240 Hz what is the wavelength?

**Step 1:**

What information are we given?

Answer:

frequency = f = 240 Hz

speed of light = c = 3.0 * 10^{8} m/s (this is a constant that you should always have even if it does not state it in the problem)

**Step ****2****:**

What is the problem asking for?

Answer: wavelength = λ

**Step ****3****:**

What formula does this question involve?

Answer: λ (f) = c

**Step ****4****:**

How do we fill in the numbers for the formula?

Answer: λ (240 Hz) = 3.0 * 10^{8} m/s

**Step ****5****:**

How do we rearrange the equation to solve for wavelength (λ)?

Answer: Divide both sides by 240 Hz

λ (240 Hz) = | 3.0 * 10^{8} m/s |

240 Hz | 240 Hz |

**Step ****6****:**

Cross out like terms

λ (240 Hz) = | 3.0 * 10^{8} m/s |

240 Hz | 240 Hz |

**Step ****7****:**

Simplify

λ = | 3.0 * 10^{8} m/s |

240 Hz |

**Step ****8****:**

COMPLETE ANSWER: 1.25 * 10^{6} m

**VIDEO Speed of Light, Frequency, and Wavelength Calculation Demonstrated Example 2****:** If the wavelength of light is 3.7 * 10^{-7} m what is the frequency?

**Step 1:**

What information are we given?

Answer:

wavelength = λ = 3.7 * 10^{-7} m

speed of light = c = 3.0 * 10^{8} m/s (this is a constant that you should always have even if it does not state it in the problem)

**Step ****2****:**

What is the problem asking for?

Answer: wavelength = f

**Step ****3****:**

What formula does this question involve?

Answer: λ (f) = c

**Step ****4****:**

How do we fill in the numbers for the formula?

Answer:

λ (3.7 * 10^{-7} m) = |
3.0 * 10^{8} m/s |

1 |

**Step ****5****:**

How do we rearrange the equation to solve for frequency (f)?

Answer: Divide both sides by 3.7 * 10^{-7} m

(3.7 * 10^{-7} m) f = |
3.0 * 10^{8} m/s |

3.7 * 10^{-7} m |
3.7 * 10^{-7} m |

**Step ****6****:**

Cross out like terms

(3.7 * 10^{-7} m) f = |
3.0 * 10^{8} m/s |

3.7 * 10^{-7} m |
3.7 * 10^{-7} m |

**Step ****7****:**

Simplify

f = | 3.0 * 10^{8} m/s |

3.7 * 10^{-7} m |

**Step ****8****:**

COMPLETE ANSWER: 8.1 * 10^{14} Hz

**PRACTICE PROBLEMS**: Solve for the unknown wavelength or frequency. Don’t forget that you have the speed of light constant = c = 3.0 * 10^{8} m/s.

If the wavelength of a light wave is 14.6m, what is the frequency?

Answer: 2.0 * 10^{7} Hz

If the frequency of a light wave is 0.89 Hz, what is the wavelength?

Answer: 3.4* 10^{8} m

If the wavelength of a light wave is 6.7 * 10^{-5} m, what is the frequency?

Answer: 4.5 * 10^{12} Hz

If the frequency of a light wave is 5.3 * 10^{12} Hz, what is the wavelength?

Answer: 5.7 * 10^{-5} m