Question bank: Waves: Speed on Strings

A transverse wave travels along a stretched rope with a speed of 20 m/s. The tension in the rope is increased to twice the original value, keeping all other conditions constant. Considering that the linear density of the rope is 0.01 kg/m, calculate the new wave propagation speed. Explain, based on the theory of waves in ropes, how tension and linear density affect the propagation speed.

A sinusoidal wave travels along a 5.0 m long steel rope. The wave is generated by a device that vibrates the rope at a frequency of 100 Hz. The linear mass of the rope is 0.02 kg/m. Considering the properties of steel (density 7.8 g/cm³ and Young's modulus 200 GPa), calculate: 1) The propagation velocity of the wave in this rope. 2) The tension needed to keep the rope stretched and allow the wave to propagate at the calculated velocity. Remember that the velocity of a transverse wave on a rope is given by V = sqrt(T/μ), where V is the wave velocity, T is the tension in the rope, and μ is the linear mass of the rope. Additionally, the tension in the rope is related to the Young's modulus and the deformation by Hooke's Law, T = Y * (ε * L), where Y is the Young's modulus, ε is the deformation, and L is the initial length of the rope.

A guitar string of negligible mass and length L, attached at one end, is tensioned by a constant force T. A pulse is generated at the free end and propagates along the string. Considering that the speed of wave propagation in a string is given by v = sqrt(T/μ), where μ is the linear mass density of the string, and that the linear mass density is given by μ = m/L, where m is the mass of the string, describe the theoretical calculation process to determine the wave propagation speed on this guitar string. Then, relate this theoretical calculation to a practical experiment that could be performed in a laboratory to measure the wave speed on the string, considering that the masses and dimensions of the string are known. Discuss possible sources of error and how to minimize them in the experiment.

In a Physics laboratory, students conduct an experiment to study the speed of waves propagating on a rope. A rope with a length of 5m and a total mass of 0.25 kg is stretched by a tension force applied at its ends. The applied tension force is 250 N. Consider that the experiment occurs without external influences (such as friction). Based on this information: a) Determine the linear density (µ) of the rope in kg/m. b) Calculate the speed of the wave propagating along this rope. c) If the oscillation frequency of the source generating the wave on the rope is 50 Hz, what will be the wavelength generated in this experiment?

During a practical physics class, a group of students decides to investigate the effect of different materials on the speed of wave propagation. For this, they use two ropes of the same length (2 meters) and the same tension (50N), but made of different materials: one made of nylon, with a linear density of 0.02 kg/m, and the other made of cotton, with a linear density of 0.03 kg/m. Without the aid of any device or digital application, they generate a pulse at one end of each rope and measure the time it takes for the pulse to reach the other end. Assuming that the wave propagation in both ropes is affected only by the linear density of the material, which of the two ropes, nylon or cotton, will have a longer pulse propagation time? Justify your answer, taking into consideration the fundamental concepts, theories, and principles of wave propagation in ropes.