A long string having a cross- sectional area `0.80 mm^2` and density `12.5 g cm^(-3)` is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (c ) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (d) What is the velocity of this particle at this instant ?

Explanation

To solve the problem step by step, we will break it down into parts (a), (c), and (d) as per the question.

### Given Data:
- Cross-sectional area \( A = 0.80 \, \text{mm}^2 = 0.80 \times 10^{-6} \, \text{m}^2 \)
- Density \( \rho = 12.5 \, \text{g/cm}^3 = 12.5 \times 10^{3} \, \text{kg/m}^3 \)
- Tension \( T = 64 \, \text{N} \)
- Frequency \( f_0 = 20 \, \text{Hz} \)
- Maximum displacement \( y = 1.0 \, \text{cm} = 0.01 \, \text{m} \)
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