please solve with values given and show each step A sinusoidal transverse wave i

Question

please solve with values given and show each step

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure below shows a plot of the displacement as a function of position at time t = 0. The x axis is marked in increments of 20 cm and the y axis is marked in increments of 0.5 cm. The string tension is4.4 N, and its linear density is 25 g/m.

(a) Find the amplitude.
m

(b) Find the wavelength.
m

(c) Find the wave speed.
m/s

(d) Find the period of the wave.
s

(e) Find the maximum speed of a particle in the string.
m/s

(f) Complete the equation describing the traveling wave, in which x and y are in meters and t is in seconds.
y(x, t) = sin( x + t + )

Explanation / Answer

Amplitude A = 5*0.5 cm = 2.5 cm

wavelength lambda = 4*20 cm =80 cm

wavespeed v = sqrt(T/miu) =13.266 m/s

lambda = v*T

T = 0.0603 seconds

Vmax = omega*A =(2*pi/T)*A =(2*pi/0.0603)*0.025= 2.605 m/s

eq of wave travveling in positive x direction is

Y(x,t) = A*sin[2*pi*(x/lambda -t/T) +fi]

Eq of wave travelling in the NEGATIVE x direction is

Y(x,t) = A*sin(2*pi*(-x/lambda -t/T) +fi) = A*sin[2*pi(x/lambda +t/T) +fi] =0.025*sin(7.85*x +104.2*t +fi) meter

From the initial conditions at t=0 (from the picture) we can determine fi

0.02 =0.025*sin(fi)    fi = 53.13 deg =0.927 rad

Y(x,t)= 0.025*sin(7.85x +104.2t +0.927)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.