Answer: The wavelength changes by a factor of [tex]\frac{1}{2}[/tex]
Explanation:
The equation of the speed [tex]v[/tex] of a wave is:
[tex]v=\lambda f[/tex]
Where:
[tex]v[/tex] is the speed, that remains unchanged
[tex]\lambda[/tex] is the wavelength
[tex]f[/tex] is the frequency
Isolating [tex]\lambda[/tex] we have:
[tex]\lamba=\frac{v}{f}[/tex]
Now, if we increase the frequency by a factor of 2:
[tex]\lambda=\frac{v}{2f}[/tex]
[tex]\lambda=\frac{1}{2} \frac{v}{f}[/tex] This means the wavelength changes by a factor of [tex]\frac{1}{2}[/tex]
