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A 2 m long rope having a mass of 26 grams is stretched with a tension of 50 N. It is set to periodic
motion with frequency of 30 Hz and amplitude of 3 cm. considering zero amplitude at t = 0 seconds
and wave motion along the +x-axis. Find
a|. amplitude (A).
b|. wave speed (v).
c|. angular frequency().
d|. period (T).
e|. wavelength().

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onyebuchinnaji

(a) The amplitude of the wave is 3 cm.

(b) The speed of the wave is 19.6 m/s

(c) The angular frequency is 653.72 rad/s.

(d) The period of the wave is 0.0096 s.

(e) The wavelength of the wave is 0.392 m.

Speed of the wave

The speed of the wave is calculated as follows;

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

where;

  • μ is mass per unit length = (0.26 kg)/(2 m) = 0.13 kg/m
  • T is tension

[tex]v = \sqrt{\frac{50}{0.13} } \\\\v = 19.6 \ m/s[/tex]

Angular frequency

ω = v/r

ω = v/A

ω = 19.6/0.03

ω = 653.72 rad/s

Period of the wave

[tex]T = \frac{2\pi }{\omega } \\\\T = \frac{2\pi }{653.72} \\\\T = 0.0096 \ s[/tex]

Wavelength

v = fλ

λ = v/f

λ = 19.6/50

λ = 0.392 m

Learn more about wavelength here: https://brainly.com/question/10728818

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