The equation of a transverse wave traveling along a very long string is y 6.0 sin (0.020px 4.0pt), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string

given

y=6.0sin (0.020px + 4.0pt)

the general wave equation moving in the positive directionis

y (x, t) = ymsin (kx - ? t)

a) the amplitude is

ym = 6.0cm

b)

we have the angular wave number as

k = 2p / ?

or

? = 2p / 0.020p

=1.0*102cm

c)

the frequency is

f = ?/2p

= 4p/2p

= 2.0 Hz

d)

the wave speed is

v = f?

= (100cm) (2.0Hz)

= 2.0*102cm/s

e)

since the trignometric function is (kx - ? t), sothe wave propagates in th - x direction

f)

the maximum transverse speed is

umax = 2pfym

= 2p (2.0Hz) (6.0cm)

= 75cm/s

g)

we have

y (3.5cm, 0.26s) = 6.0cmsin[0.020p (3.5) + 4.0p (0.26) ]

= - 2.0cm