Question

A transverse traveling wave on a cord is represented by, where D and x are in meters and t is in seconds.

Answer 1

Answer with Explanation:

We are given that a transverse travelling wave on a cord is represented by

$D=0.51sin(6.1x+76t)$

Where D and x in meters

t(in seconds)

a.General equation of transverse wave

$y=Asin(kx+\omega t)$

By comparing we get

A=0.51

$k=6.1$

$k=\frac{2\pi}{\lambda}$

Wavelength,$\lambda=\frac{2\pi}{k}=\frac{2\pi}{6.1}=1.03$

b.$\omega=76$

Frequency,$f=\frac{\omega}{2\pi}=\frac{76}{2\pi}=12.096Hz$

c.Velocity,$v=f\lambda=12.096\times 1.03=12.46m/s$

Direction:Towards negative x- axis

d.Amplitude,A=0.51 m

e.Maximum speed,$v_{max}=A\omega=0.51\times 76=38.76 m/s$

Minimum speed,$v_{min}=0$