A sinusoidal wave is traveling on a string with speed 66.0 cm/s. The displacemen
ID: 1495819 • Letter: A
Question
A sinusoidal wave is traveling on a string with speed 66.0 cm/s. The displacement of the particles of the string at x = 14 cm is found to vary with time according to the equation
y = (4.5 cm) sin[1.4 - (6.6 s-1)t].
The linear density of the string is 3.5 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) = ym sin(kx - t),
what are (c) ym, (d) k, and (e) , and (f) the correct choice of sign in front of ? (g) What is the tension in the string?
Explanation / Answer
given
wave speed, v = 66 cm/s
at x = 14 cm, y = (4.5 cm)*sin(1.4 - 6.6*t)
so, w = 6.6 rad/s
mue = 3.5 g/m = 0.0035 kg/m
a) f = w/(2*pi)
= 6.6/(2*pi)
= 1.05 hz
b) apply, v = lamda*f
==> lamda = v/f
= 66/1.05
= 62.8 cm or 0.628 m
c) ym = 4.5 cm
d) from the given equation, k*x = 1.4
k = 1.4/x
= 1.4/14
= 0.1 rad/m
e) w = 6.6 rad/s
f) "-" (negative sign)
g) apply, v = sqrt(T/mue)
==> T = v^2*mue
= 0.66^2*0.0035
= 1.5*10^-3 N