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Home » Considering the wave, Answer the following questions; (a) Are all the points in the wire oscillating at the same values of (i) frequency, (ii) phase, (iii) amplitude? Justify your answers. (b) Calculate the amplitude of a point away from one end?
Considering the wave, y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)
Answer the following questions;
(a) Are all the points in the wire oscillating at the same values of (i) frequency, (ii) phase, (iii) amplitude? Justify your answers.
(b) Calculate the amplitude of a point 0.4 \mathrm{~m} away from one end?
CBSE | Class 11 | NCERT | Physics | Waves
Considering the wave, y(x, t)=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)
Answer the following questions;
(a) Are all the points in the wire oscillating at the same values of (i) frequency, (ii) phase, (iii) amplitude? Justify your answers.
(b) Calculate the amplitude of a point 0.4 \mathrm{~m} away from one end?

(a) Because both ends of the wire are clamped, the ends act as nodes, and the entire wire vibrates as a single segment. Thus,

(i) Except at the wire’s ends, where the frequency is 0, all of the particles in the wire vibrate at the same rate.

(ii) Because all of the particles in the wire are contained in a single segment, they all have the same phase. With the exception of the nodes.

(iii) Amplitude, however, is different for different points.

(b) Given equation is,

\mathrm{y}(\mathrm{x}, \mathrm{t})=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)

For x=0.4 \mathrm{~m} and t=0

\begin{array}{l} \text { Amplitude }=\text { displacement }=0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos 0 \\ =0.06 \sin \left(\frac{2 \pi}{3} \times 0.4\right) 1 \\ =0.044 \mathrm{~m} \end{array}

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