Final answer:
This answer provides the values for amplitude, wavelength, frequency, speed, direction of propagation, maximum transverse speed, and transverse displacement for a transverse wave traveling along a string. It also explains how to calculate these values using the given equation.
Step-by-step explanation:
(a) Amplitude: The amplitude of a wave is the maximum displacement of particles in the medium from their equilibrium position. From the given equation, y = 6.8 sin(0.023px + 3.2pt), the amplitude is 6.8 cm.
(b) Wavelength: The wavelength of a wave is the distance between two consecutive points that are in phase. In this equation, the coefficient of 'x' is 0.023p, so the wavelength is given by λ = 2π/0.023p.
(c) Frequency: The frequency of a wave is the number of cycles it completes in one second. In this equation, the coefficient of 't' is 3.2p, so the frequency is given by f = 3.2p/2π.
(d) Speed: The speed of a wave is given by the product of its frequency and wavelength. So, speed = f × λ.
(e) Direction of propagation: The terms 'x' and 'y' in the equation represent the spatial dimensions of the wave. Since 'x' and 'y' have opposite signs, the wave propagates in the negative x-direction.
(f) Maximum transverse speed: The maximum transverse speed of a particle in the string can be determined by taking the derivative of the equation with respect to 't' and evaluating it at the point where the sine function reaches its maximum value.
(g) Transverse displacement at x = 3.5 cm when t = 0.26 s: To find the transverse displacement at a specific point in space and time, substitute the given values of 'x' and 't' into the equation y = 6.8 sin(0.023px + 3.2pt) and calculate the result.