a wave has a wavelength of 4.9 m and a velocity of 9.8 m/s. the medium through which this wave is traveling…

Explanation:

Step1: Recall wave - velocity formula

The wave - velocity formula is $v = f\lambda$, where $v$ is the velocity, $f$ is the frequency, and $\lambda$ is the wavelength. Initially, $v_1 = f\lambda_1$, so $f=\frac{v_1}{\lambda_1}$. Given $v_1 = 9.8$ m/s and $\lambda_1 = 4.9$ m, then $f=\frac{9.8}{4.9}=2$ Hz.

Step2: Consider the new velocity

The velocity is doubled, so $v_2 = 2v_1=2\times9.8 = 19.6$ m/s. Since the frequency remains constant ($f = 2$ Hz), and using $v = f\lambda$ again, we can find the new wavelength $\lambda_2$. Rearranging the formula for $\lambda_2$ gives $\lambda_2=\frac{v_2}{f}$.

Step3: Calculate the new wavelength

Substitute $v_2 = 19.6$ m/s and $f = 2$ Hz into the formula for $\lambda_2$. $\lambda_2=\frac{19.6}{2}=9.8$ m.

Answer:

9.8 m