A generator at one end of a very long string creates a wave given by y = A cos [

Question

A generator at one end of a very long string creates a wave given by

y = A cos [?(2.0x + 3.0t)],

and at the other end a generator creates the wave

y = A cos [?(2.0x ? 3.0t)],

where A = 4.0 cm, x is in meters, and t is in seconds.

A) What is the frequency of the waves?

B) What is the wavelength?

C) What is the magnitude of the phase velocity?

D) If the origin is at one end, and the length is adjusted so that there is a resonant standing wave on the string, what is x at the first node?

E) What is x at the second node?

F) What is x at the third node?

G) What is x at the first antinode?

Explanation / Answer

you have to remember that:

cos(a+b)+cos(a-b)=2cos(a)*cos(b)
so you some the equations above that gives you:

y=2A*cos(2pi*x)cos(3 pi*t)

for any t if cos(2pi*x)=0 the perturbation will be zero:
2pi*x=pi/2+n*pi, n is a natual number
x=0.25+n in meters that means the points with no motion are:

0.25m
-0.25m
ect ect ect....

A) f= 3/ 2 Pi = 0.4774

B) 2*pi/K =

so answer = 3.14

C)0.25 m

D)1.25

E)2.25

F)0.25/2

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