Question

1. which of the following best explains how wavelength and frequency are related for waves traveling at the same speed?

• as frequency increases, wavelength increases
• as wavelength increases, frequency increases
• as frequency increases, wavelength decreases
• wavelength and frequency are not related

clear all

Explanation:

The relationship between wavelength ($\lambda$), frequency ($f$), and speed ($v$) of a wave is given by the formula $v = \lambda f$. When the speed $v$ is constant, wavelength and frequency are inversely proportional. So, if frequency ($f$) increases, wavelength ($\lambda$) must decrease to keep the speed constant. Let's analyze each option:

• "As frequency increases, wavelength increases": This is incorrect because they are inversely proportional (when speed is constant), so an increase in frequency should lead to a decrease in wavelength.
• "As wavelength increases, frequency increases": This is also incorrect. If wavelength increases, for a constant speed, frequency should decrease (since $f=\frac{v}{\lambda}$).
• "As frequency increases, wavelength decreases": This is correct. From $v = \lambda f$, when $v$ is constant, $f=\frac{v}{\lambda}$, so as $f$ increases, $\lambda$ must decrease.
• "Wavelength and frequency are not related": This is incorrect because the wave speed formula shows a direct relationship between them (when speed is constant, they are inversely related).

Answer:

As frequency increases, wavelength decreases