Question

A string that is under 51.0 N of tension has a linear density of 5.70 g/m. A sinusoidal wave with an amplitude of 3.30 cm and a wavelength of 1.90 m travels along the string. What is the frequency of the wave?

1) 2.00 Hz
2) 3.00 Hz
3) 4.00 Hz
4) 5.00 Hz

Answer 1

The frequency of the sinusoidal wave traveling along the string is approximately 49.82 Hz, which means none of the provided options are correct.

Step-by-step explanation:

To determine the frequency of a sinusoidal wave traveling along a string, we can use the formula for the wave speed v on a string, which is given by √(F/μ), where F is the tension in the string and μ is the linear mass density. Once we have the wave speed, we can calculate the frequency f using the relationship v = fλ, where λ is the wavelength of the wave.

The linear mass density μ is given as 5.70 g/m, which we convert to kilograms per meter (0.00570 kg/m). The tension F in the string is 51.0 N and the wavelength λ is 1.90 m.

First, we calculate the wave speed:

√(51.0 N / 0.00570 kg/m) ≈ 94.65 m/s

Now, to find the frequency f:

94.65 m/s / 1.90 m ≈ 49.82 Hz

Therefore, none of the provided options (2.00 Hz, 3.00 Hz, 4.00 Hz, 5.00 Hz) are correct; the actual frequency of the wave is approximately 49.82 Hz.