A 3m slinky rests on a table with a student holding each end. The students laterally shake the ends of the slinky to generate transverse waves. The student on the left shakes the slinky at 4 Hz with a 5 cm amplitude and the student on the right shakes it at 3 Hz with a 7 cm amplitude.

Question

What is the maximum deflection of the string, from its resting position, between the students in cm?

Ok so I'm assuming they mean slinky, since there isn't any string in the problem...

but still, what is that supposed to mean? How is deflection measured?

Answer 1

They mean how far from straight the sum of the waves moves the string.
Now if there would be just one wave you could say y = A sin (wt -kx)
and the max would be A
if there was one from the left and one from the right then you have
y = A sin (wt - kx - phi) + B sin (Wt + kx - psi)
the max will be whenever both sines are +1 or -1 and will be A+B which is 8 (or -8)

Answer 2

a + b is 12 isnt it. not 8, so answer would be 12?

Answer 3

An easier way to interpret the maximum deflection as being 12cm is simply to think of the superposition of wave A and wave B meeting constructively. Wave A (5cm) + Wave B (7cm) would result in a 12cm superposed amplitude.