Question

A wave traveling on a Slinky® that is stretched to 4 m takes 2.4 s to travel the length of the Slinky and back again. (a) What is the speed of the wave? (b) Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?

a) 3.33 m/s, 1.25 Hz
b) 2.00 m/s, 2.50 Hz
c) 1.67 m/s, 1.50 Hz
d) 4.00 m/s, 1.88 Hz

Answer 1

The speed of the wave traveling on the stretched Slinky is 1.67 m/s, and the frequency of the standing wave created on the Slinky is approximately 1.04 Hz.

Step-by-step explanation:

(a) What is the speed of the wave?

The speed of a wave can be calculated by dividing the distance traveled by the time taken. In this case, the wave travels twice the length of the Slinky, which is 4 meters, and takes 2.4 seconds. Therefore, the speed of the wave is 4 m ÷ 2.4 s = 1.67 m/s.

(b) At what frequency must the Slinky be oscillating?

In a standing wave, the frequency can be determined based on the number of antinodes and nodes. In this case, the standing wave has three antinodes and four nodes. The frequency can be calculated using the formula: frequency = (wave speed) ÷ (wavelength), where wavelength = 2 × (distance between adjacent nodes). The distance between adjacent nodes is (length of Slinky) ÷ (number of nodes + 1) = 4 m ÷ (4 + 1) = 0.8 m. Therefore, the wavelength is 2 × 0.8 m = 1.6 m. Plugging in the values, the frequency is (1.67 m/s) ÷ (1.6 m) ≈ 1.04 Hz.