Answer:
2.48 m is the length of the rope.
Explanation:
Cycle period is 321
Time is 20 second
Wave travels at speeds = 26.4 m/s
We know that,
[tex]\text { Frequency }=\frac{1}{T} \text { (For one cycle) }[/tex]
Frequency required for 321 complete cycle in 20 seconds is
[tex]\text { Frequency }(f)=\frac{321}{20}[/tex]
Frequency = 16.05 hz
We know that,
[tex]\text { Wavelength }=\frac{\text { wave velocity }}{\text { frequency }}[/tex]
[tex]\lambda=\frac{v}{f}[/tex]
λ = wavelength, the distance between "wave crests" (m)
v = wave velocity, the "speed" that waves are moving in a direction (m/s)
f = frequency, (cycles/ or Hz)
[tex]\lambda=\frac{26,4}{16.05}[/tex]
λ = 1.65 m
As per given question "length of the rope has three equal length segment"
[tex]\mathrm{Length of the rope}=\frac{3}{2} \lambda[/tex]
[tex]\mathrm{Length of the rope }=\frac{3}{2} \times 1.65[/tex]
[tex]\mathrm{Length of the rope}=1.5 \times 1.65[/tex]
Length of the rope = 2.48 m
Therefore, length of the rope is 2.48 m.
