The frequency of the standing wave can be calculated using the formula:
f = v / λ
where f is the frequency, v is the speed of the wave, and λ is the wavelength of the wave.
First, we need to calculate the wavelength of the waves generated by each student. The wavelength can be calculated using the formula λ = 2L, where L is the distance between the two students (in this case, 3m).
The wavelength generated by the student on the left shaking at 4Hz can be calculated as:
λ1 = v / f1
λ1 = 30m/s / 4Hz
λ1 = 7.5m
Similarly, the wavelength generated by the student on the right shaking at 3Hz can be calculated as:
λ2 = v / f2
λ2 = 30m/s / 3Hz
λ2 = 10m
For a standing wave with a node centered between the two students, the wavelength of the standing wave must be 3m (distance between the students). Therefore, the frequency of the standing wave can be calculated as:
f = v / λ
f = 30m/s / 3m
f = 10Hz
Therefore, the students must shake the slinky at a frequency of 10Hz in order to create a standing wave with a node centered between them.
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 4Hz with a 5cm amplitude and the student on the right shakes it at 3Hz with a 7cm 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 30m/s?
1 answer