Math Problem Statement

If the speed of a wave is constant, what happens to the frequency of the wave if the wavelength increases? A.The frequency increases then decreases. B.The frequency remains constant. C.The frequency increases. D.The frequency decreases.

Solution

The relationship between the speed vv, frequency ff, and wavelength λ\lambda of a wave is given by the equation:

v=fλv = f \lambda

If the speed vv of the wave is constant and the wavelength λ\lambda increases, the frequency ff must decrease to keep the product fλf \lambda constant. This is because the two variables are inversely related: when one increases, the other must decrease for the speed to remain the same.

Thus, the correct answer is:

D. The frequency decreases.

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

  1. How does the speed of sound change with temperature, assuming constant frequency?
  2. What is the relationship between energy and frequency in a wave?
  3. How do amplitude and frequency relate to each other in terms of wave properties?
  4. What happens to a wave's frequency if both speed and wavelength are doubled?
  5. Can a wave's frequency change without affecting its speed?

Tip: Remember, frequency and wavelength have an inverse relationship if the wave speed stays constant.

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Math Problem Analysis

Mathematical Concepts

Wave Physics
Frequency
Wavelength
Speed of Waves

Formulas

v = fλ (Wave speed formula)

Theorems

Inverse Relationship between Frequency and Wavelength

Suitable Grade Level

Grades 9-12