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Answer:
1.1975 m
Note: This answer was not rounded and given as exact. Please round according to your directions if necessary.
Explanation:
To determine the wavelength of the transverse wave on the slinky, we need to use the given information about the number of peaks over a certain distance.
The wavelength (λ) is the distance between two consecutive peaks (or troughs) of a wave. The given data states that there are 5 peaks over a horizontal distance of 4.79 meters.
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To find the wavelength, we need to understand that the distance between 5 peaks includes 4 complete wavelengths. This is because the first peak starts the count, and each additional peak represents the end of one wavelength and the start of another.
1. Total number of wavelengths:
Since 5 peaks correspond to 4 complete wavelengths
[tex]\text{Number of wavelengths}=5-1=\boxed{4}[/tex]
Wavelength (λ):
[tex]\lambda = \dfrac{\text{Total Distance}}{\text{Number of Wavelengths}}[/tex]
[tex]\lambda = \dfrac{4.79 \text{ m}}{4}[/tex]
[tex]\therefore \lambda = \boxed{1.1975 \text{ m}}[/tex]
The wavelength of the transverse wave on the slinky is 1.1975 meters.