Final answer:
To produce transverse waves with a speed of 49.5 m/s on a string with a length of 4.30 meters and a mass of 0.0600 kg, the required tension in the string is approximately 34.19 N. This calculation uses the formula T = v² μ by identifying the linear mass density and plugging in the given speed and computed density.
Step-by-step explanation:
Calculating the Required Tension in a Stretched String for Transverse Waves
When producing transverse waves on a string, the wave speed is determined by the tension and the linear mass density of the string. The linear mass density (μ) is the mass per unit length and can be calculated by dividing the total mass of the string by its length. In this scenario, you have a string with a length of 4.30 meters and a mass of 0.0600 kg, so μ can be derived as follows:
μ = mass / length = 0.0600 kg / 4.30 m = 0.01395 kg/m
Using the wave speed equation for a string, v = √(T / μ), and rearranging for tension (T), the equation becomes T = v² μ. Substituting the given wave speed of 49.5 m/s and the calculated μ, we find the required tension:
T = (49.5 m/s)² * 0.01395 kg/m = tension required
Performing the calculation,
T = 2450.25 * 0.01395 = tension required
T = 34.19 N
Therefore, to produce transverse waves with a speed of 49.5 m/s on the given string, the required tension in the string would be approximately 34.19 N.