A rope has a density of 7.5 g/cm3 and a cross-sectional area of 2.0 cm2.

When the rope is subjected to a tension of 100 N, and one end is vibrated up and down with a frequency of 25 Hz, what is the (a) velocity of the transverse wave in the rope and (b) wavelength in Chapter the rope?​

Explanation:

The density of a rope, d = 7.5 g/cm³

The cross-sectional area of the rope, A = 2 cm²

The tension in the rope, T = 100 N

One end is vibrated up and down with a frequency of 25 Hz.

(a) The velocity of the transverse wave in the rope is given by :

Mass per unit length will be :

[tex]\mu=\rho A\\\\=7.5\times 2\\\\=15\ cm[/tex]

So,

[tex]v=\sqrt{\dfrac{T}{\mu}}\\\\v=\sqrt{\dfrac{100}{15}}\\\\v=2.58\ m/s[/tex]

(b) Let [tex]\lambda[/tex] is the wavelength of the rope. So,

[tex]v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{2.58}{25}\\\\\lambda=0.103\ m[/tex]

So, the velocity of the transverse wave in the rope is 2.58 m/s and the wavelength is 0.103 m.

(a) "2.58 m/s" would be the velocity.

(b) "0.103 m" would be the wavelength.

According to the question,

Density,

Cross-sectional area,

Tension,

(a)

Mass per unit:

→ [tex]\mu = \rho A[/tex]

      [tex]= 7.5\times 2[/tex]

      [tex]= 15 \ cm[/tex]

then,

The velocity of transverse wave will be:

→ [tex]v = \sqrt{\frac{T}{\mu} }[/tex]

     [tex]= \sqrt{\frac{100}{15} }[/tex]

     [tex]= 2.58 \ m/s[/tex]

(b)

The wavelength of rope will be:

→ [tex]v = f \lambda[/tex]

or,

→ [tex]\lambda = \frac{v}{f}[/tex]

     [tex]= \frac{2.58}{25}[/tex]

     [tex]= 0.103 \ m[/tex]

Thus the above answers are correct.

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Assignment Summary
For this assignment, you will construct a personal dietary plan that is reflective of your current diet in terms of its nutritional value. Before creating this plan, you will conduct research to explore current dietary guidelines. You will also evaluate personal barriers, and internal and external influences, to setting nutritional goals, and making food choices. You will use a food log to monitor the progress of meeting these goals. This log will help track your eating habits over the course of five days. After your entire dietary plan is constructed, you will evaluate whether healthy daily nutritional values are being met. You will then participate in a small group discussion.

1
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Q 5-6 Select Physiology.

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