Question

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

(a) Determine the wavelength.
(b) Determine the frequency.
(c) Determine the velocity (magnitude and direction). (
d) Determine the amplitude.
(e) Determine the maximum and minimum speeds of particles of the cord.

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=(2\pi)/(\lambda)`

Wavelength,
`\lambda=(2\pi)/(k)=(2\pi)/(6.1)=1.03`

b.
`\omega=76`

Frequency,
`f=(\omega)/(2\pi)=(76)/(2\pi)=12.096Hz`

c.Velocity,
`v=f\lambda=12.096* 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* 76=38.76 m/s`

Minimum speed,
`v_(min)=0`