Math for practice: 1. A transverse sine wave of amplitude 10 cm and wavelength 200 cm travels from left to right along a long horizontal string with a speed 100cm/s. Take the origin at the left end. At time t=0. the left end of the string is at the origin and is moving downward i. Find the frequency, angular frequency, and propagation constant 10.5 Hz, 3.14/s 0.031/cm] ii. What is the equation of the wave? [y=10sin((pi x)/(100)-pi t)] iii. What is the equation of motion of the left end of the string? [y=-10sin(pi t)]

Let's go through each part of the problem step by step.### i. Finding the Frequency, Angular Frequency, and Propagation ConstantGiven:- Amplitude cm- Wavelength cm- Speed cm/s- Time with the left end moving downward**Frequency (f):**The frequency is given by: **Angular Frequency (ω):**The angular frequency is given by: **Propagation Constant (k):**The propagation constant is given by: So, the values are:- Frequency - Angular Frequency - Propagation Constant ### ii. Equation of the WaveThe general form of a sine wave is: Given that at , the left end (origin) is at the origin and moving downward, we can set the phase constant .Thus, the equation of the wave is: ### iii. Equation of Motion of the Left End of the StringThe left end of the string is at the origin (x = 0). Therefore, the equation of motion for the left end is: So, the equation of motion of the left end of the string is: In summary:- The frequency is .- The angular frequency is .- The propagation constant is .- The equation of the wave is \( y(x, t) = 10 \sin\left(\frac{\pi x}{100} - \pi t\right) \).- The equation of motion of the left end of the string is \( y = -10 \sin(\pi t) \).