Question

Two similar waves X and Y travel through the same medium. Wave X has a frequency of 200 hertz and a wavelength of 35 meters. Wave Y has a frequency of 700 hertz. What is the wavelength for wave Y?(1 point)
Responses

122.5 meters
122.5 meters

10 meters
10 meters

4,900,000 meters
4,900,000 meters

0.1 meter

Answer 1

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**.