The relationship between wavelength, speed and frequency of a wave is given by
[tex]\lambda= \frac{v}{f} [/tex]
where
[tex]\lambda[/tex] is the wavelength
v the speed
f the frequency
For the first wave, we can write
[tex]\lambda_1 = \frac{v}{f_1} [/tex]
while for the second wave
[tex]\lambda_2 = \frac{v}{f_2} [/tex]
where v is the same for two waves, since they have same speed. The first wave has twice the frequency of the second, so
[tex]f_1 = 2 f_2[/tex]
So we can rewrite the wavelength of the first wave as
[tex]\lambda_1 = \frac{v}{2 f_2}= \frac{1}{2} \frac{v}{f_2}= \frac{1}{2} \lambda_2 [/tex]
which means that the correct answer is
3. the first has half the wavelength of the second
