Answer:
1. The first has half the wavelength of the second
Explanation:
Consider λ₁ and λ₂ be the wavelengths of the first and second wave respectively.
Consider f₁ be the frequency of the first wave. According to the problem,
Frequency of the second wave, f₂ = f₁/2 ....(1)
The relation between speed, frequency and wavelength of the wave is:
v = λf
Here v is speed of the wave, λ is wavelength and f is frequency.
So, the speed of first wave is:
v₁ = λ₁f₁
And, speed of second wave is:
v₂ = λ₂f₂
But according to the problem:
v₁ = v₂
λ₁f₁ = λ₂f₂
[tex]\frac{\lambda_{1} }{\lambda_{2} }=\frac{f_{2} }{f_{1} }[/tex]
Put equation (1) in the above equation.
[tex]\frac{\lambda_{1} }{\lambda_{2} }=\frac{f_{1} }{2f_{1} }[/tex]
[tex]\frac{\lambda_{1} }{\lambda_{2} }=\frac{1}{2}[/tex]
λ₂ = 2λ₁ or λ₁ = λ₂/2
