Question bank: Waves: Speed on Strings

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Question 1:

Hard

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.

Waves: Speed on Strings

Exam Style

Theorical Question

Contextualized Question

Question 2:

Easy

A guitar string has a linear mass of 5 g/m and is under a tension of 100 N. If a wave is generated on the string by plucking and propagates at a speed of 20 m/s, calculate the linear density of the string. Consider that the tension in the string is given by the formula T = mu * v^2, where T is the tension, mu (Greek letter) is the linear density of the string, and v is the wave speed on the string.

Waves: Speed on Strings

Multidisciplinary Question

Question 3:

Very Easy

A tension wave is generated in a stretched steel rope whose modulus of elasticity is 2.1 x 10^11 N/m^2. The linear density of the rope is 0.003 kg/m. Considering that the propagation velocity of a wave in a medium is given by V = √(T/μ), where T is the tension in the rope and μ is the linear density of the rope, calculate the propagation velocity of the wave in this steel rope.

Waves: Speed on Strings

Contextualized Question

Calculus Question

Question 4:

Very Hard

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.

Waves: Speed on Strings

Multidisciplinary Question

Question 5:

Medium

In a Physics laboratory, a group of students uses a rope with linear density of 0.02 kg/m, stretched with a tension of 50 N, to perform experiments with waves. Calculate the speed of the wave on the rope and select the correct alternative:

Waves: Speed on Strings

IARA TIP

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