Question

question 8 of 25
a wave travels at a constant speed. how does the wavelength change if the frequency is reduced by a factor of 4? assume the speed of the wave remains unchanged.

a. the wavelength increases by a factor of 4.
b. the wavelength does not change.
c. the wavelength decreases by a factor of 16.
d. the wavelength decreases by a factor of 4.

Explanation:

Step1: Recall wave - speed formula

The wave - speed formula is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength.
We can rewrite it as $\lambda=\frac{v}{f}$.

Step2: Analyze the change in wavelength

Let the initial frequency be $f_1$ and the initial wavelength be $\lambda_1$, so $\lambda_1=\frac{v}{f_1}$.
The new frequency $f_2=\frac{1}{4}f_1$. Since $v$ is constant, the new wavelength $\lambda_2=\frac{v}{f_2}=\frac{v}{\frac{1}{4}f_1}=4\times\frac{v}{f_1}$.
Since $\lambda_1 = \frac{v}{f_1}$, we have $\lambda_2 = 4\lambda_1$.

Answer:

A. The wavelength increases by a factor of 4.