9.03 Wave Calculations

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Wave Calculation Problems

In your notebook, solve the following 7 wave calculations. Be sure to show your work. Then, check your answers.

1. What is the frequency of an x-ray that has a wavelength of 1.5×10^-9 m?
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Wavelength = 1.5×10^-9 m

      Speed = 3.0×10⁸ m/s

      Frequency = ?

      Formula: λ = v / ƒ

   2. Rearrange equation and input the values to solve.

      λ = v / ƒ

      ƒ = v / λ

      ƒ = (3.0×10⁸ m/s) / (1.5×10^-9m)

      ƒ = 2.0×10¹⁷ Hz

      Answer: The frequency of the x-ray is 2.0×10¹⁷ Hz.




2. The frequency of a microwave is 1.2×10⁹ Hz. What is its wavelength?
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Frequency = 1.2×10⁹ Hz

      Speed = 3.0×10⁸ m/s

      Wavelength = ?

      Formula: λ = v / ƒ

   2. Input the values to solve.

      λ = v / ƒ

      λ = (3.0×10⁸ m/s) / (1.2×10⁹ Hz)

      λ = 2.5×10^-1 m OR 0.25 m

      Answer: The wavelength of the microwave is 0.25 m.




3. You cannot see high frequency ultraviolet light rays, but they can damage your eyes and skin. Calculate the frequency of an ultraviolet light wave that has a wavelength of 3.0×10^-7 m.
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Wavelength = 3.0×10^-7 m

      Speed = 3.0×10⁸ m/s

      Frequency = ?

      Formula: λ = v / ƒ

   2. Rearrange the formula equation. Input the values to solve.

      λ = v / ƒ

      ƒ = v / λ

      ƒ = (3.0×10⁸ m/s) / (3.0×10^-7 m)

      ƒ = 1.0×10¹⁵ Hz

      Answer: The frequency of the UV ray is 1.0×10¹⁵ Hz.




4. A radio station broadcasts a wave at a frequency of 1.0×10⁶ Hz. What is its wavelength?
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Frequency = 1.0×10⁶ Hz

      Speed = 3.0×10⁸ m/s

      Wavelength = ?

      Formula: λ = v / ƒ

   2. Input the values to solve.

      λ = v / ƒ

      λ = (3.0×10⁸ m/s) / (1.0×10⁶ Hz)

      λ = 3.0×10² m

      Answer: The frequency of the radio wave is 3.0×10² m.




5. The speed of sound is 340 m/s. What is the wavelength of sound waves produced by a guitar string vibrating at 440 Hz?
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Frequency = 440 Hz

      Speed = 340 m/s

      Wavelength = ?

      Formula: λ = v / ƒ

   2. Input the values to solve.

      λ = v / ƒ

      λ = 340 m/s / 440 Hz

      λ = 7.73×10^-1 m

      Answer: The wavelength of the sound waves from the guitar strings is 7.73×10^-1 m.




6. Sound travels at approximately 1,500 m/s in sea water. How far will a sonar pulse travel in 120s?
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Speed = 1,500 m/s

      Time = 120 s

      Distance = ?

      Formula: v = d/t

   2. Rearrange the formula and input the values to solve.

      v = d/t

      d = v×t

      d = (1,500 m/s)(120 s)

      d = 180,000 m OR 1.8×10² m

      Answer: The sonar pulse will travel 180,000 m in 120 seconds.




7. It takes 12s for a sonar pulse to travel to travel 15 km. What is the speed of the sonar pulse? (HINT: Convert km to m)
   
   
   How to Solve:
   1. Identify the known and unknown values and the formula needed to solve the problem.

      Distance = 15 km

      Time = 12 s

      Speed = ?

      Formula: v = d/t

   2. Convert 15 km to meters.

      15 km = 15,000 m

   3. Input the values to solve.

      v = d/t

      v = (15,000 m)(12 s)

      v = 1,250 m/s OR 1.25×10³ m/s

      Answer: The speed of the sonar pulse is 1,250 m/s or 1.25×10³ m/s.