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 87 m/s. At t = 0, the string particle at x = 0 has a transverse displacement of 4.3 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 16 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

Here, y(x, t) = ym*sin(kx ± t + )

=>   dy/dt = ± * ym*cos(kx ± t + )

Since the wave is moving along the positive x direction

=>   0.043 =   ym*sin( )

Also,   = pi/2

=>   ym =   0.043 m

Also,   * ym = 16

=>      = 372.09 rad/sec

a)   the frequency of the wave = (372.09/(2*3.14))    =   59.25 Hz

b)    wavelength of the wave =   87/59.25   =   1.468 m

c)    ym =   0.043 m

d)    k   =   /c   = 372.09/87   =   4.276 m-1

e)        =   372.09 rad/sec

f)        =   pi/2

g)     the correct choice of sign in front of =     minus (-) sign .

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