Question

A student hangs a slinky over the edge of a stairwell. The slinky is stretched so that it is just above the ground. The student sends a pulse down the slinking and measures the speed to be 18m/s. The student then vibrates the slinky with a frequency of 4.5 Hz and notices that 4 nodes produced. The end near the floor is an open end and the end where the student his holding the slinking is a fixed end.] How high is the stairwell?
a) Calculate the wavelength of the slinky. (4.0 m)
b) Draw a well labelled diagram of the situation. (because of one open end, there are 3.5 loops)
c) Calculate the height of the stairwell. (h = 7 wavelength quarters, 7/4λ = h, h = 7.0 m)

Answer 1

The drawing of the wave in the slinky shows the node and antinode

in the form of a standing wave pattern.

The correct responses;

• a) 4.0 meters

• b) Please find attached the drawing of the wave motion in the slinky

• c) 7.0 m

Method used to arrive at the response above:

Given parameters;

The speed of the wave pulse through the slinky, v = 18 m/s

The frequency with which the student vibrates the slinky, f = 4.5 Hz

Number of nodes in the slinky, n = 4 nodes

a) Wavelength of the slinky λ:

The wavelength of the slinky, λ, is given as follows;

$\displaystyle \lambda = \mathbf{ \frac{v}{f}}$

Therefore;

$\displaystyle \lambda = \frac{18 \, m/s }{4.5 \, Hz} = \mathbf{4.0 \, m}$

• The wavelength of the wave formed on the slinky, λ = 4.0 meters

b) Drawing of a well labelled diagram of the situation:

The attached drawing of the situation shows the wavelength of the

wave equal to the distance between three consecutive nodes, N

The number of loops = 3 complete loops + Half of a loop = 3.5 loops

c) To calculate for the height of the stairwell:

The length of the wavelength, λ = Length of two complete loops

Height of the stairwell = 3.5 loops

2 loops = λ

Therefore;

$\displaystyle Height \ of \ stairwell = \frac{\lambda}{2 } \times 3.5 = \mathbf{1.75 \cdot \lambda}$

Which gives;

• Height of the stairwell, h = 1.75 × 4.0 m = 7.0 m

Learn more about wave motion here:

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