Question

In a physics lab, a rope is observed to make 240 complete vibrational cycles in 15s. the length of the rope is 2.8m and the measurements are made for the 6th harmonic (with six equal length sections). Determine the speed of the waves in the rope. V = 0.0625 x 2.8 = 0.175 m/s This is what I did- my teacher said to find the wavelength of one wave- which wouldn't be 2.8​​ ​

Answer 1

The speed of the waves in the rope is 268.8m/s.

Step-by-step explanation:

To determine the speed of the waves in the rope, we need to find the wavelength of one wave. In this case, the rope is divided into six equal length sections, so the wavelength of one wave will be equal to the length of one section (2.8m) multiplied by the number of sections (6).

Therefore, the wavelength is 2.8m * 6 = 16.8m. To find the speed of the waves, we can use the formula v = λf, where v is the speed, λ is the wavelength, and f is the frequency. Since the number of cycles in 15s gives us the frequency (240 cycles/15s = 16 Hz), we can calculate the speed.

Plugging in the values, v = 16.8m * 16Hz

= 268.8m/s.