P17_007.PDF

ωt ). A negative sign

is used before the ωt term in the argument of the sine function because the wave is traveling in the

positive x direction. The angular wave number k is k =2 π/λ =2 π/ (0 . 10 m) = 62 . 8m − 1 and the

angular frequency is ω =2 πf =2 π (400 Hz) = 2510 rad / s. Here λ is the wavelength and f is the

frequency. The amplitude is y m =2 . 0cm. Thus

y ( x, t )=(2 . 0 cm) sin 62 . 8m − 1 x

−

− 2510 s − 1 t .

(b) The (transverse) speed of a point on the cord is given by taking the derivative of y :

u ( x, t )= ∂y

∂t =

−

ωy m cos( kx

−

ωt )

which leads to a maximum speed of u m = ωy m = (2510 rad / s)(0 . 020 m) = 50 m / s.

T = ω

k = 2510 rad / s

62 . 8m − 1

=40m / s .

7. (a) We write the expression for the displacement in the form y ( x, t )= y m sin( kx

v = λ