Question

two ropes are identical. a wave traveling through the first rope has a frequency of 1.5 hertz and a wavelength of 6 meters. what is the frequency of a wave in the second rope if its wavelength is 2 meters? (1 point)
9 hertz
1.5 hertz
3 hertz
4.5 hertz

Explanation:

Step1: Recall wave speed formula

The speed of a wave \( v \) is given by \( v = f \lambda \), where \( f \) is the frequency and \( \lambda \) is the wavelength. Since the ropes are identical, the wave speed \( v \) is the same in both ropes.

Step2: Calculate speed in first rope

For the first rope, \( f_1 = 1.5 \, \text{Hz} \) and \( \lambda_1 = 6 \, \text{m} \). Using \( v = f_1 \lambda_1 \), we get \( v = 1.5 \times 6 = 9 \, \text{m/s} \).

Step3: Find frequency in second rope

For the second rope, \( \lambda_2 = 2 \, \text{m} \) and \( v = 9 \, \text{m/s} \). Using \( f_2 = \frac{v}{\lambda_2} \), we substitute \( v = 9 \) and \( \lambda_2 = 2 \): \( f_2 = \frac{9}{2} = 4.5 \, \text{Hz} \).

Answer:

4.5 hertz (corresponding to the option: 4.5 hertz)