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.
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?
a + b is 12 isnt it. not 8, so answer would be 12?
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.
Well, it seems like the slinky is having a wavy time there! To answer your question, deflection in this case refers to the maximum displacement of the slinky from its resting position to its highest point (or lowest point) due to the wave motion. In other words, it's how far the slinky goes up or down from its original position.
In this scenario, we have two students shaking the slinky at different frequencies and amplitudes. To find the maximum deflection between the students, we need to consider the highest displacement caused by each student.
The student on the left shakes the slinky at 4 Hz with a 5 cm amplitude. So, the maximum displacement caused by the left student is 5 cm (since that's the amplitude).
The student on the right shakes it at 3 Hz with a 7 cm amplitude. Therefore, the maximum displacement caused by the right student is 7 cm.
To find the overall maximum deflection between the students, we need to add the displacements caused by each student. So, the maximum deflection would be the sum of the maximum displacements: 5 cm + 7 cm = 12 cm.
Therefore, the maximum deflection of the slinky between the students would be 12 cm. So imagine that slinky going up and down like it's doing the wave at a stadium. Hope that clears things up!
In the context of this problem, the term "deflection" refers to the maximum displacement or maximum amplitude of the waves on the slinky from its resting or equilibrium position. To better understand this, let's break down the problem step by step.
First, let's identify the information given:
- The left student shakes the slinky at a frequency of 4 Hz with an amplitude of 5 cm.
- The right student shakes the slinky at a frequency of 3 Hz with an amplitude of 7 cm.
Now, let's draw a diagram to visualize the situation. Imagine a slinky with the left student at one end and the right student at the other end. The waves generated by the students will propagate along the slinky.
To find the maximum deflection between the students, we need to consider a few concepts from wave mechanics.
1. Wave velocity (v):
The wave velocity is determined by the properties of the medium through which the waves travel. In this case, since we are dealing with a slinky, the velocity depends on the tension in the slinky and the mass per unit length of the slinky. However, the problem does not provide information about these properties, so we cannot calculate the wave velocity directly.
2. Wavelength (λ):
The wavelength of a wave is the distance between two consecutive points in phase. In this case, we are dealing with transverse waves, so the wavelength refers to the distance between successive crest or trough points. To calculate the wavelength, we can use the formula:
λ = v / f
where:
- λ is the wavelength
- v is the wave velocity (unknown for this problem)
- f is the frequency
3. Wave superposition:
When two waves that have different frequencies and amplitudes intersect, they will superpose at any given point. The resulting amplitude at a particular point is determined by the principle of superposition, which states that the displacements at that point due to the individual waves add up vectorially.
Now, getting back to the specific question of finding the maximum deflection between the students, we need to consider the superposition of the two waves.
Since wave velocity (v) is not provided, we have no way of calculating the wavelength (λ) or determining the specific positions of crest and trough points. Therefore, we cannot directly find the maximum deflection using the given information.
However, if we assume that both students are shaking the slinky perfectly in phase, meaning the crest and trough of one wave align with the crest and trough of the other wave, then the maximum deflection would be the sum of the individual amplitudes:
Maximum deflection = Amplitude of student on the left + Amplitude of student on the right
= 5 cm + 7 cm
= 12 cm
So, based on this assumption, the maximum deflection between the students would be 12 cm.
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)