Final answer:
To find the tension in the string, we use the wave speed formula with the given mass, length, frequency, and wavelength. The calculated tension in the string is approximately 55.65 Newtons.
Step-by-step explanation:
This has asked how to calculate the tension T in a stretched string that measures 2.07 m in length and has a mass of 20.5 g, which oscillates at 440 Hz producing transverse waves with a wavelength of 17.1 cm. To calculate the tension, we can use the formula for the speed of a wave on a string (v) given by v = √(T/μ), where T is the tension and μ (mu) is the linear mass density of the string. The speed of the wave is also given by the product of frequency (f) and wavelength (λ), so v = f × λ. Plugging our values into these equations, we have 20.5 g = 0.0205 kg2.07 m (length of the string)0.0205 kg / 2.07 m = 0.0099 kg/m (μ)440 Hz (frequency)17.1 cm = 0.171 m (wavelength). The speed of the wave on the string is v = 440 Hz × 0.171 m = 75.24 m/s. Now we can rearrange the wave speed formula to solve for tension (T): T = μ × v^2. Substituting our known values gives the tension T as: T = 0.0099 kg/m × (75.24 m/s)^2T = 55.65 N. Therefore, the tension in the string is approximately 55.65 Newtons.