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)

Question

Responses

1.5 hertz
1.5 hertz

4.5 hertz
4.5 hertz

3 hertz
3 hertz

9 hertz

Answer 1

To find the frequency of the wave in the second rope, we can use the wave speed formula:

\[ \text{Wave speed} (v) = \text{frequency} (f) \times \text{wavelength} (\lambda) \]

For the first rope, we have:

• Frequency \( f_1 = 1.5 , \text{Hz} \)
• Wavelength \( \lambda_1 = 6 , \text{m} \)

Calculating the wave speed in the first rope:

\[ v = f_1 \times \lambda_1 = 1.5 , \text{Hz} \times 6 , \text{m} = 9 , \text{m/s} \]

Assuming the wave speed in both ropes is the same (since they are identical), we can use this wave speed to find the frequency of the wave in the second rope.

For the second rope:

• Wavelength \( \lambda_2 = 2 , \text{m} \)

Using the same wave speed:

\[ v = f_2 \times \lambda_2 \]

Setting the wave speed equal to 9 m/s:

\[ 9 , \text{m/s} = f_2 \times 2 , \text{m} \]

Solving for \( f_2 \):

\[ f_2 = \frac{9 , \text{m/s}}{2 , \text{m}} = 4.5 , \text{Hz} \]

Thus, the frequency of the wave in the second rope is 4.5 hertz.