Final answer:
To find the parameters of the standing wave on the string, we need to analyze the given equation for displacement. The parameters include the speed of the waves, the wavelength of the standing wave, and the period of the standing wave.
Step-by-step explanation:
The given equation for the displacement of the string, y = 1.2m * sin(π/2 - x) * sin(34πt), represents a standing wave on the string. To find the parameters, we need to analyze the equation.
(a) The speed of the waves on the string can be determined from the equation v = λf, where v is the speed, λ is the wavelength, and f is the frequency. In the fundamental harmonic, there is one node and one antinode. From the given equation, we can deduce that λ = 2x, where x is the distance from the first node to the second node. The frequency can be obtained from the equation f = n * f0, where n is the mode number and f0 is the frequency of the fundamental mode. As the string is vibrating at its natural frequency, the fundamental mode corresponds to n = 1. Therefore, f0 is the frequency of the sound produced by the string in its fundamental harmonic. By comparing the given equation with the standard equation for a standing wave, y = Asin(kx)sin(ωt), we can equate the coefficients to find the values of k and ω. With the values of k and ω, we can calculate the values of v, λ, and f.
(b) The wavelength of the standing wave can be determined using the formula λ = 2x, where x is the distance from one node to the adjacent node. This distance can be obtained by analyzing the equation y = 1.2m * sin(π/2 - x) * sin(34πt) and finding the value of x for which sin(π/2 - x) becomes zero.
(c) The period of the standing wave can be determined using the formula T = 1/f, where T is the period and f is the frequency. From part (a), we can obtain the frequency of the standing wave in the fundamental harmonic, and then calculate the period using the formula T = 1/f.