The speed of a wave is given by the equation v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency. If we want to double the speed of the wave while keeping the frequency constant, we can rearrange the equation to solve for the new wavelength.
Let's assume the initial speed of the wave is v1, the initial wavelength is λ1, and the frequency is f. The initial equation is v1 = λ1f.
If we double the speed of the wave, the new speed will be 2v1. The frequency remains unchanged, so it is still f. We can now solve for the new wavelength, λ2.
2v1 = λ2f
Dividing the equation by 2v1, we get:
1 = (λ2f) / (2v1)
Rearranging the equation, we find:
λ2 = (2v1) / f
Therefore, to double the speed of the wave while maintaining the frequency, the new wavelength (λ2) should be equal to (2v1) / f, where v1 is the initial speed and f is the frequency of the wave.