A transverse sinusoidal wave is moving along a string in the positive direction

Question

A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of 93 m/s. At t = 0, the string particle at x = 0 has a transverse displacement of 4.1 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 18 m/s. (a) What is the frequency of the wave? (b) What is the wavelength of the wave? If the wave equation is of the form y(x, t) = ym sin(kx ± t + ), what are (c) ym, (d) k, (e) , (f) , and (g) the correct choice of sign in front of ?

Explanation / Answer

Amplitude is A = 0.041 m

Vmax = A*w = 18

then angular frequency w = 18/A = 18/0.041 = 439 rad/s

frequency f =w/(2*2*pi) = 439/(2*3.142) = 69.85 Hz

wavelength lamda = v/f = 93/69.85 = 1.33 m

ym = 0.041 m

k =2*pi/lamda = 2*3.142/1.33= 4.72 m^-1

w = 439 rad/s

at t = 0 and t = 0

y = 0.041 = 0.041*sin(0+0+)

sin() = 1 = sin(90)

= 90 degrees

since the wave is passing along positive x-direction then sign infront of w is negative

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