Question

A rope has one end tied to a vertical support. You hold the other end so that the rope is horizontal. If you move the end of the rope back and forth with a frequency of 4 Hz, the transverse wave you produce has a wavelength of 0.5 m. What is the speed of the wave in the rope?4 m/s0.13 m/s8 m/s2 m/s

Answer 1

• The speed of the wave in the rope is 2 m/s

Step-by-step explanation:

1. Data:

a) ν = 4 Hz

b) λ = 0.5 m

c) s = ?

2. Physical principles and formula:

The propagation of waves in a rope is a classical example of transverse waves: the pulse is inflected in the vertical direction and the wave travels in the horizontal direction, i.e. the pulse or vibration is perpendicular to the motion of the media particles.

The equation that relates speed (s), wavelength (λ), frequency (ν) is:

• distance = speed × time

• wavelength = speed × period

• wavelenfth = speed / frequency

• λ = s / ν

• meter = (meter/second) / second⁻¹

• m = (m /s) / s⁻¹

3. Solution:

• λ = s / ν⇒ s = λ·ν

• s = 0.5 m × 4 Hz = 2 m/s