Question

You generate a wave in a spring, stretched out on the floor, by oscillating your hand back and forth at a frequency of 1.6 Hz. The wave has a 1.5m wavelength. If the wave takes 2.9s to travel to the other end of the spring and back to your hand, what is the length of the stretched spring?

Answer 1

Answer on Question #43402 – Physics – Other

Question.

You generate a wave in a spring, stretched out on the floor, by oscillating your hand back and forth at a frequency of $1.6\mathrm{Hz}$. The wave has a $1.5\mathrm{m}$ wavelength. If the wave takes 2.9s to travel to the other end of the spring and back to your hand, what is the length of the stretched spring?

Given:

$$\begin{array}{l} v = 1.6\mathrm{Hz} \\ \lambda = 1.5\mathrm{m} \\ t = 2.9\mathrm{s} \\ \end{array}$$

Find:

$$L = ?$$

Solution.

For wave propagation in the medium we have the following equality:

$$\lambda = c \cdot T = \frac{c}{v}$$

$c$ is the speed of wave in medium;

$T$ is the period of oscillation.

Therefore, $c = \lambda \cdot v$

The length of spring is equal to:

$$L = c \cdot t = \lambda \cdot v \cdot t$$

Calculate:

$$L = 1.5 \cdot 1.6 \cdot 2.9 = 6.96\mathrm{m}$$

Answer. $L = \lambda \cdot v \cdot t = 6.96\mathrm{m}$

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