physics help!!!! the sunillg a ation describing a transverse wave on a string is

Question

physics help!!!! the sunillg a ation describing a transverse wave on a string is 11. I The equation y(x, t) = ( 1.50 mm) sin [ (157 s-1)I-(41.9 ml)x). Find (o) the wavelength. frequency, and amplitude of this wave. () Find (a) the wavelength, frequency, and amplitude of this wave, (b) the speed and direction of motion of the wave, and (c) the transverse displacement of a point on the string when t = 0.100 s and at a posi- tion x = 0.135 m. 12- Transverse waves are traveling on a long string that is under a ten-

Explanation / Answer

the general equation describing the transverse wave is

y(x,t) = A*sin(wt-kx)

so comparing the given equation with the above equation

A is the amplitude then amplitude is A = 1.5 mm = 1.5*10^-3 m

frequency f = w/(2*pi) = 157/(2*3.142) = 25 Hz

wavelength lamda = 2*pi/K = (2*3.142)/(41.9) = 0.1499 m

B) speed of the wave is v = dx/dt = (1.5*10^-3*157)*cos(157t-41.9x)

direction is along +x-axis

C) transverse dispalcement y = 1.5*10^-3*sin((157*0.1)-(41.9*0.135)) = -0.8699 mm

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