7.

(a) We write the expression for the displacement in the form y(x, t) = y

m

sin(kx

− 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 = 2π/λ = 2π/(0.10 m) = 62.8 m

−1

and the

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

m

= 2.0 cm. Thus

y(x, t) = (2.0 cm) sin

62.8 m

−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.

(c) The speed of the wave is

v =

λ

T

=

ω

k

=

2510 rad/s

62.8 m

−1

= 40 m/s .