Given: L = 5.0 m

48 cycles in 20 seconds

The frequency refers to how often a point on the medium undergoes back-and-forth vibrations; it is measured as the number of cycles per unit of time. In this case, it is

f = (48 cycles) / (20 seconds) = 2.4 Hz

The period is the reciprocal of the frequency.

T = 1 / (2.4 Hz) = 0.417 seconds

The wavelength of the wave is related to the length of the rope. For the fourth harmonic as pictured in this problem, the length of the rope is equivalent to two full wavelengths. That is, L = 2 • W where W is the wavelength. Rearranging the equation and substituting leads to the following results:

W = 0.5 • L = 0.5 • (5.0 m) = 2.5 m

The speed of a wave can be calculated from its wavelength and frequency using the wave equation:

v = f • W = (2.4 Hz) • (2.5 m) = 6.0 m/s