Question

Two waves have the same speed. the first has twice the frequency of the second. compare the wavelengths of the two waves. 1. the second has square root two times the wavelength of the first. 2. the have the same wavelength. 3. the first has half the wavelength of the second. 4. the second has half the wavelength of the first. 5. the first has twice the wavelength of the second.

Answer 1

The relationship between wavelength, speed and frequency of a wave is given by
$\lambda= \frac{v}{f}$
where
$\lambda$ is the wavelength
v the speed
f the frequency

For the first wave, we can write
$\lambda_1 = \frac{v}{f_1}$
while for the second wave
$\lambda_2 = \frac{v}{f_2}$
where v is the same for two waves, since they have same speed. The first wave has twice the frequency of the second, so
$f_1 = 2 f_2$
So we can rewrite the wavelength of the first wave as
$\lambda_1 = \frac{v}{2 f_2}= \frac{1}{2} \frac{v}{f_2}= \frac{1}{2} \lambda_2$

which means that the correct answer is
3. the first has half the wavelength of the second