Final answer:
The speed of the wave propagating along the wire is 5 m/s, calculated by using the wavelength of 2.5 m and the frequency of 2 Hz.
Step-by-step explanation:
The question asks us to find the speed of a wave propagating along a wire, given that there are eight nodes on a 17.5 m long wire and the source makes 20 complete oscillations in 10 seconds.
To determine the wave speed, we need to understand that standing waves are formed by the interference of two waves traveling in opposite directions with the same speed. In a standing wave on a string that is fixed at both ends, the distance between two consecutive nodes is half a wavelength (λ/2). Since there are eight nodes, including the ends, there are seven half wavelengths in the 17.5 m long wire. Therefore, one complete wavelength would be 17.5 m / 7 = 2.5 m.
To find the frequency (f), we use the information that there are 20 oscillations in 10 seconds, thus the frequency is 20 oscillations / 10 seconds = 2 Hz. The speed (v) of the wave is then calculated using the formula v = f λ. Plugging in the values, we get v = 2 Hz × 2.5 m = 5 m/s.