Question

A sinusoidal wave is traveling on a string with speed 34.9 cm/s. The displacement of the particles of the string at x = 5.9 cm is found to vary with time according to the equation
y = (3.9 cm) sin[1.2 - (7.1 s^-1)t].
The linear density of the string is 4.8 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t) = y_m sin(kx - ωt),
what are (c) y_m, (d) k, and (e) ω, and (f) the correct choice of sign in front of ω? (g) What is the tension in the string?

Answer 1

here

amplitude A = 3.9cm = 0.039m = ym

= -7.1rad/sec

= 2f----------(1)

7.1 = 2x3.14xf

so frequency f = 1.13Hz

period T = 1/f

       T = 1/1.13 = 0.88sec

angular wave number k = 1.2rad/m

to find the wavelength we make use of the formula ie

k = 2 / ----------(2)

so = 2/k

       = 2(3.14) / 1.2

therefore = 5.23cm

to calculate the tension in the string we make use of the formula

V = T /m--------(3)

here m is the hav(3) we linear density = 4.8x10^-3kg/m

squarnf eqn (3) we have

(V)^2 = T / m

(0.349)^2 = T / (4.8x10^-3)

T = 5.84x10^-4N