Watching your fish swim in their tank, you notice that when one fish repeatedly

Question

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.

Explanation / Answer

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

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