Период колебаний волны равен корню квадратного уравнения:
4x2-20x+25=0. Определите время, за которое волна совершит 900 колебаний. Также рассчитайте частоту колебаний.
To solve this problem, we need to first find the solutions to the given quadratic equation 4x2-20x+25=0. This can be done using the quadratic formula, which states that the solutions to the equation ax2+bx+c=0 are given by x=(-b±√(b^2-4ac))/2a. In this case, a=4, b=-20, and c=25, so the solutions are x=5/2 and x=5. However, since we are looking for a time and not just a value for x, we will only use the positive solution x=5. Now, we know that the time it takes for a wave to complete one full cycle is equal to the period, T, which is given by T=1/f, where f is the frequency. In our case, since the wave is completing 900 cycles, we can set T=900/f. Since we also know that the time it takes for the wave to complete one cycle (the period) is equal to 5 seconds (from our solution for x), we can set 5=900/f and solve for f. This gives us a frequency of 180 Hz. Therefore, the time it will take for the wave to complete 900 cycles is 5 seconds, and the frequency of the wave is 180 Hz.
