Watching your fish swim in their tank you notice that when o

Watching your fish swim in their tank, you notice that when one fish repeatedly jumps, it causes a standing wave given by the time-independent function f(x)=asin(bx), with a = 0.015 m and b = 18.6 m1 .

Part A

If the tank is 0.96 m long, determine the position of the first node, beginning with the node at one end of the tank.

Part B

If the tank is 0.96 m long, determine the position of the second node, beginning with the node at one end of the tank.

Part C

If the tank is 0.96 m long, determine the position of the third node, beginning with the node at one end of the tank.

Solution

comare the given function with standard time independent wave equation

         y = A sin ( 2 pi x / (lamda) )

So

    2 pi / lamda = b

wavelength (lamda ) = 2 pi / b = 2 pi / ( 18.6) =0.337.

A)

The position of first node is at the origin. that meant at one end of tank.

B) second node is at lamda / 2 = ( 0.337) /2 = 0.168 m

c) Third node is at 0.337 m