Question

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 hertz with a 5cm amplitude and the student on the right shakes it at 3 hertz with a 7cm amplitude.
The student's waves travel at the same speed and the maximum deflection of the string, from its resting position, between the students is 12 cm. The students agree to make a standing wave with a node centered between them, so they are the antinodes. At what frequency in hertz must they shake the slinky if the speed of a wave in the slinky is 30 m/s?

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