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)

10 meters

0.1 meter

4,900,000 meters

122.5 meters

Explanation:

Step1: Recall wave speed formula

The speed of a wave \( v \) is given by \( v = f\lambda \), where \( f \) is frequency and \( \lambda \) is wavelength. Since waves X and Y travel through the same medium, their speeds are equal (\( v_X = v_Y \)). So, \( f_X\lambda_X = f_Y\lambda_Y \).

Step2: Rearrange formula for \( \lambda_Y \)

From \( f_X\lambda_X = f_Y\lambda_Y \), we get \( \lambda_Y=\frac{f_X\lambda_X}{f_Y} \).

Step3: Substitute values

Given \( f_X = 200\space Hz \), \( \lambda_X = 35\space m \), \( f_Y = 700\space Hz \). Substitute into the formula: \( \lambda_Y=\frac{200\times35}{700} \).

Step4: Calculate the value

\( \frac{200\times35}{700}=\frac{7000}{700} = 10\space meters \).

Answer:

10 meters