A transverse harmonic wave travels on a rope according to the following expressi

Question

A transverse harmonic wave travels on a rope according to the following expression:

y(x,t) = 0.17sin(2.3x + 17.1t)

The mass density of the rope is = 0.148 kg/m. x and y are measured in meters and t in seconds.

6)

At x = 3.2 m and t = 0.44 s, what is the velocity of the rope? (watch your sign)

m/s

7)

At x = 3.2 m and t = 0.44 s, what is the acceleration of the rope? (watch your sign)

m/s2

8)

What is the average speed of the rope during one complete oscillation of the rope?

m/s

9)

In what direction is the wave traveling?

+x direction

-x direction

+y direction

-y direction

+z direction

-z direction

10)

On the same rope, how would increasing the wavelength of the wave change the period of oscillation?

the period would increase

the period would decrease

the period would not change

Explanation / Answer

6.

Velocity of the rope is given by

Vy=dY/dt =2.907cos(2.3x+17.1t)

at x=3.2 m and t=0.44 s

Vy=(2.907)cos(2.3*3.2+17.1*0.44)

Vy=-1.975 m/s

7.

acceleration of the rope is

ay=-49.7sin(2.3x+17.1t)

ay=-49.7sin(2.3*3.2+17.1*0.44)=-36.47 m/s2

8.

W=17.1 rad/sec

time period

T=2pi/W=2pi/17.1=0.3674 s

average speed is

Vavg=4A/T=4*0.17/0.3674=1.85 m/<

9.

-x direction

10.

the period would increase.

since f=V/lambda

T=1/f

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