Question

At the position r = 0 A (meters) 30 t (seconds) 10 Which wave function corresponds best to the diagram? 2. y= A sin ko- 1. y = A sin ko - (25) -- () 2. y = A sin(kx - (39) +- (63) sin (er - () - ()] [62-(19) --() [63-(3) --() sin ka - ()--(*) 7., = Asin ka- (19) :-()] – A sin kr- () :-(-) 9. y = A sin k=-()- () 10. y = A sin k3 - (25) - (5)

Answer 1

Given equation is

$y = A sin(kx - \omega t - \phi)$

A = 1 for this case.

For the given graph we have x = 0

So, the equation becomes,

$y =sin(- \omega t - \phi)$

In the given graph, we have

y(20) = 0 for t = 20

So, we substitute 20 in each of these expressions and check for which values we will get y(20) = zero.

Doing that, we see

y(20) = 0 for options 2, 7, 8 and 10.

Now we see that the value of the function will be negative at t= 10 from the graph.

Doing the substitution for the remaining options

y(10) = -ve only for 2 and 10.

Now

y(3.5) at t= 3.5 for option 2 = 0

But for option 10 is not 0

From the graph, we get y(3.5) is not zero, the value equals zero for y(5) So, option 2 is also not correct.

Hence, the graph is the representation of option 10

$y =A sin(kx- \frac{2\pi}{15} t - \frac{4\pi}{3})$-----------------------------------------------------------(OPTION 10)