9.03 Wave Calculations

Review

Before we get into the math for waves, let's review some of the properties of waves. Do you remember the definitions for the following parts of a wave?

Wavelength Check It!

Frequency Check It!

We have one more property to add to our understanding of waves, and it's one that you learned earlier in this course when we studied motion – velocity or speed. Remember, velocity is simply distance divided by time. It's sometimes written as the following equation: v = d/t

All waves travel with a specific velocity, so we will be using this concept to solve math problems. Specifically, electromagnetic waves which include radio waves, light waves, x-rays, and UV rays all travel at the same speed which is 3×10⁸ m/s.

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Formula

Now, let's relate the wavelength, frequency, and velocity of a wave together in a mathematical formula. First let's review the symbol and unit for each of these measurements.

• Wavelenth
  
  • Symbol: λ
  • Unit of measurement: meters (m)


• Frequency
  
  • Symbol: ƒ
  • Unit of measurement: Hertz (Hz)


• Velocity
  
  • Symbol: v
  • Unit of measurement: distance/time (usually m/s)

These are related together using the following equation: v = λƒ

Look at the following tabs to see some example problems using this formula to solve problems!

(HINT: Remember, velocity can be calculated if necessary using v = d/t. Also remember that if you are dealing with an electromagnetic wave, the velocity is 3×10⁸ m/s)

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Example Problem 1

Example 1:
The frequency of the wave broadcast by a radio station is 1.2×10⁶ Hz. What is the wavelength of the station's wave?

How to Solve:

1. First identify the known and unknown values.
   Frequency = 1.2 106 Hz
   Speed = 3.0×10⁸ m/s
   Wavelength = ?


2. Next, input these values into the formula and solve.
   λ = v / ƒ
   λ = (3×10⁸ m/s) / (1.2×10⁶ Hz)
   λ = 2.5×10² m

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Example Problem 2

Problem 2:
Visible light waves that our eyes see as the color red have a wavelength of about 6.7×10^-7 meters. What is the frequency of these waves?

How to Solve:

1. First identify the known and unknown values.
   Wavelength = 6.7×10^-7 m
   Speed = 3.0×10⁸ m/s
   Frequency = ?


2. Rearrange the equation so that ƒ is on the left side of the equation by itself.
   λ = v / ƒ
   ƒ = v / λ
   


3. Input the values and solve.
   ƒ = (3×10⁸ m/s) / (6.7×10^-7 m)
   ƒ = 4.5×10¹⁴ Hz

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