To find the wavelength of wave Y, we can use the relationship between wave speed (v), frequency (f), and wavelength (λ), which is given by the equation:
\[ v = f \cdot \lambda \]
First, we need to calculate the wave speed using wave X:
For wave X:
- Frequency (\(f_x\)) = 200 Hz
- Wavelength (\(λ_x\)) = 35 m
Using the equation, we can find the speed:
\[ v = f_x \cdot λ_x = 200 , \text{Hz} \cdot 35 , \text{m} = 7000 , \text{m/s} \]
Now that we have the wave speed, we can use it to find the wavelength of wave Y.
For wave Y:
- Frequency (\(f_y\)) = 700 Hz
Now we use the wave speed and the frequency of wave Y to find its wavelength:
\[ v = f_y \cdot λ_y \]
This gives us:
\[ λ_y = \frac{v}{f_y} = \frac{7000 , \text{m/s}}{700 , \text{Hz}} = 10 , \text{meters} \]
Thus, the wavelength for wave Y is 10 meters.