Math Problem Statement

A student observes two transverse waves with different frequencies. Wave A has a frequency of 5 waves per second, and Wave B has a frequency of 10 waves per second.

Which statement best describes the pattern between frequency and wavelength for these waves? A.Wave B has a longer wavelength than Wave A. B.Wave B has a shorter wavelength than Wave A. C.Both waves have the same wavelength. D.The wavelength is not affected by the frequency.

Solution

The correct answer is:

B. Wave B has a shorter wavelength than Wave A.

Explanation:

The relationship between frequency (ff) and wavelength (λ\lambda) is given by the wave equation: v=fλv = f \cdot \lambda where vv is the wave speed.

Assuming both waves travel at the same speed, a higher frequency will correspond to a shorter wavelength, and a lower frequency will correspond to a longer wavelength. Since Wave B has a higher frequency (10 waves per second) than Wave A (5 waves per second), it will have a shorter wavelength than Wave A.

Would you like further details or have any questions?

Related Questions:

  1. How does wave speed affect the relationship between frequency and wavelength?
  2. If Wave A’s frequency doubled, how would its wavelength change?
  3. What is the relationship between energy and frequency for transverse waves?
  4. How can we calculate the wavelength if we know wave speed and frequency?
  5. Why is wavelength inversely proportional to frequency in wave equations?

Tip: For waves in the same medium, increasing frequency always results in a decrease in wavelength.

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Math Problem Analysis

Mathematical Concepts

Wave frequency
Wavelength
Inverse relationship between frequency and wavelength

Formulas

v = f * λ

Theorems

Inverse relationship of frequency and wavelength in a given medium

Suitable Grade Level

Grades 8-10