A sinusoidal transverse wave is traveling along a string in the negative directi
ID: 1397087 • Letter: A
Question
A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure shows a plot of the displacement as a function of position at time t = 0; the y intercept is 4.0 cm. The string tension is 3.0 N, and its linear density is 35 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and(d) period of the wave. (e) Find the maximum transverse speed of a particle in the string.If the wave is of the form
y(x,t) = ym sin(kx - ?t + ?),
what are (f) k, (g) ?, and (h) ?, and (i) the correct choice of sign in front of ??
Explanation / Answer
from tha diagram given that,
ampitude ymax=4cm
tension F=3N
linear density rho=m/l=35g/m
a)
amplitude=ymax=4cm=0.04m
b)
wave length ,lambda=40cm=0.4 m
c)
wave speed v=sqrt(F/rho)
=sqrt(3/35*10^-3)
=9.26 m/sec
d)
T=lambda/v
=0.4/9.26
=0.0432 sec
e)
y(x,t)=ymax*sin(kx-wt+phi)
dy/dt=ymax*w*cos(kx-wt+phi)
here,
vmax=w*ymax
=(2pi/T)*ymax
=(2pi/0.0432)*(0.04)
=5.81 m/sec
f)
k=2pi/lambda
=2pi/0.4
=15.7 m^-1
g)
w=2pi/T
=2pi/0.0432
=145.37 rad/sec
h)
y(x,t)=ymax*sin(kx-wt+phi)
at t=0 sec, x=0
0.04=0.04*sin(k*0-w*0+phi)
sin(phi)=1
====> phi=pi/2 or 90 degrees
i)
sice wave is moving along negative direction of an x-axis
the sign infront of w is "-ve"