To find the wavelength of wave Y, we can use the wave speed formula:
\[ v = f \times \lambda \]
where:
- \( v \) is the wave speed,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
First, we need to determine the wave speed using wave X:
For wave X:
- Frequency \( f_X = 200 \) Hz
- Wavelength \( \lambda_X = 35 \) meters
Calculating the wave speed (\( v \)) of wave X:
\[ v = f_X \times \lambda_X = 200 , \text{Hz} \times 35 , \text{m} = 7000 , \text{m/s} \]
Now we can use the wave speed for wave Y, which has a frequency of \( f_Y = 700 \) Hz. We will use the same wave speed:
\[ v = f_Y \times \lambda_Y \]
Substituting the values we have:
\[ 7000 , \text{m/s} = 700 , \text{Hz} \times \lambda_Y \]
Now we solve for \( \lambda_Y \):
\[ \lambda_Y = \frac{7000 , \text{m/s}}{700 , \text{Hz}} = 10 , \text{meters} \]
Therefore, the wavelength for wave Y is 10 meters.