Question

a. Find the speed of a wave on a string given by y(x,t)=(3.00 mm) sin [(7.0/s)t -(4.00/m)x) ]

. b. What can you do to increase the speed of the wave?

c. What is the vertical speed of the string at a point located 0.2m away from the origin at time 0.3s?

d. A wave given by y(x,t)=(3.00 mm) sin [(7.0/s)t -(4.00/m)x+pi/2 ] is created on another identical string. What is different and what is the same in these two waves? Describe as completely as possible.

Answer 1

Ans:-

y(x,t)=(3.00 mm) sin [(7.0/s)t -(4.00/m)x) ]

a]v = w/k

w=7/s, k=4/m

v= 7/4 =1.75m/s

b]as wavelength increase so wave number decrease

speed of wave also increases

c] y(x,t)=(3.00 mm) sin [(7.0/s)t -(4.00/m)x) ]

u = dy/dt = (3.00mm) cos[(7.0/s)t – (4.00/mx)]*7

x=0.2m, t= 0.3s

u= 3.*10^-3 *7 cos(7*0.3 – 4*0.2)

u=21*10^-3*0.9997

u= 0.021m/s

d]These waves have the same angular frequency w and thus same frequency f, same angular wave number k and same wavelength and same amplitude ym, thay have same speed, thay travel same direction. They differ by constant angle π/2 which we call phase constant. These waves are said to be out of phase by π/2