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.
The students agree to make a standing wave with a node centered between them, so they are the antinodes. At what frequency in Hz must they shake the slinky if the speed of a wave in the slinky is 30 m/s?
To create a standing wave with a node centered between them, the students need to shake the slinky at a frequency that satisfies the following condition:
f = (n * v) / (2L)
where f is the frequency, n is the number of nodes, v is the velocity of the wave, and L is the length of the slinky.
In this case, n = 1 (one node centered between the students), v = 30 m/s (the speed of the wave in the slinky), and L = 3 m (the length of the slinky).
Substituting these values into the equation:
f = (1 * 30 m/s) / (2 * 3 m)
f = 15 m/s / 6 m
f = 2.5 Hz
Therefore, the students must shake the slinky at a frequency of 2.5 Hz to create the desired standing wave.