Two different types of rope with different properties are fused together to make one long rope when a wave transfers from the first type of rope to the second type of rope the wavelength becomes 1/4 of what it was before the transfer. What is true about the speed of the wave.
According to the wave equation, the speed (v) of a wave is given by the product of the wavelength (λ) and the frequency (f):
v = λ * f
In this case, when the wave transfers from the first type of rope to the second type, the wavelength becomes 1/4 of what it was originally. Let's denote the original wavelength as λ1 and the new wavelength as λ2.
λ2 = λ1 / 4
Since the frequency of the wave does not change during the transfer, we can rewrite the equation for speed as:
v1 = λ1 * f
v2 = λ2 * f
Dividing the second equation by the first one, we have:
v2 / v1 = (λ2 * f) / (λ1 * f)
v2 / v1 = λ2 / λ1
Substituting the given values for λ2 and λ1, we get:
v2 / v1 = (λ1 / 4) / λ1
v2 / v1 = 1 / 4
Therefore, the speed of the wave (v2) when it transfers to the second type of rope is one-fourth (1/4) of the speed of the wave (v1) in the first type of rope.