To find the frequency of the wave in the second rope, we can use the wave relationship formula:
\[ \text{wave speed} (v) = \text{frequency} (f) \times \text{wavelength} (\lambda) \]
First, calculate the wave speed in the first rope using its frequency and wavelength:
For the first rope:
- Frequency (\(f_1\)) = 1.5 Hz
- Wavelength (\(\lambda_1\)) = 6 m
Thus, the wave speed (\(v\)) in the first rope is: \[ v = f_1 \times \lambda_1 = 1.5 , \text{Hz} \times 6 , \text{m} = 9 , \text{m/s} \]
Now, we know the wave speed in the second rope is the same since the ropes are identical.
For the second rope, the wavelength is given as:
- Wavelength (\(\lambda_2\)) = 2 m
To find the frequency (\(f_2\)) of the wave in the second rope, use the wave speed we calculated: \[ v = f_2 \times \lambda_2 \] Rearranging the equation gives us: \[ f_2 = \frac{v}{\lambda_2} \] Substituting the known values: \[ f_2 = \frac{9 , \text{m/s}}{2 , \text{m}} = 4.5 , \text{Hz} \]
Thus, the frequency of the wave in the second rope is 4.5 hertz.