Final answer:
To find the propagation velocity of a transverse wave on a rope, use the formula velocity equals wavelength divided by period. With a wavelength of 58 cm and a period of 7.3 s, the wave's propagation velocity is 7.95 cm/s.
Step-by-step explanation:
When dealing with a transverse wave on a rope, one vital property to determine is the wave's propagation velocity, which indicates how fast the wave travels along the rope. To calculate this, we require the wave's wavelength and period. The wavelength (λ) is the distance between consecutive points that are in phase, such as two adjacent crests or troughs, and the period (T) is the time it takes for one complete cycle of the wave to pass a given point.
The formula for the propagation velocity (v) of a wave is given by the product of its wavelength (λ) and its frequency (f), which is the inverse of the period (T). So, v = λ * f = λ / T. Given that the wavelength of the transverse wave on a thin rope is 58 cm and the period is 7.3 s, the propagation velocity can be calculated as follows:
v = λ / T = 58 cm / 7.3 s = 7.95 cm/s (or 0.0795 m/s when converted to meters per second).