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Answer :
The speed of the transverse wave on the Slinky is calculated using the formula for wave speed on a stretched string, [tex]v = \(\sqrt{\frac{T}{\mu}}\)[/tex], and is found to be 6.46 m/s.
To determine the speed of the transverse wave on the Slinky, we must understand that the wave speed (v) on a stretched string or Slinky is given by [tex]v = \(\sqrt{\frac{T}{\mu}}\),[/tex] where T is the tension in the Slinky and [tex]\(\mu\)[/tex] is the linear mass density. Since the Slinky is stretched horizontally, the entire weight of the Slinky contributes to the tension.
The tension T is given by the force exerted on the Slinky, which is 2.0 N. The linear mass density [tex]\(\mu\)[/tex] is the mass per unit length of the Slinky, determined by dividing the mass of the Slinky by its length when stretched. The separation between the adjacent coils is 7 cm, so the total stretched length (L) is 185 coils [tex]\(\times\)[/tex] 7 cm/coil.
First, convert the coil separation to meters: 7 cm = 0.07 m. Now, multiply this by the number of coils to find the length: [tex]L = 185 \(\times\) 0.07 m = 12.95 m[/tex]. Next, find the linear mass density [tex]\(\mu\)[/tex] by dividing the mass of the Slinky (0.62 kg) by the length: [tex]\(\mu = \frac{0.62\,kg}{12.95\,m} = 0.0479\,kg/m\)[/tex].
The final step is to calculate the wave speed using the formula:
[tex]v = \(\sqrt{\frac{T}{\mu}}\) = \(\sqrt{\frac{2.0\,N}{0.0479\,kg/m}}\) = \(\sqrt{41.75\,m^2/s^2}\) = 6.46 m/s.[/tex]
The speed of the transverse wave on the Slinky is 6.46 m/s.
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