Question

He mass per unit length (sometimes written as μ) of the heavy white string provided is 0.004 kg/m.Calculate and report the tension in the string.

1) Using the above information, calculate the predicted velocity of waves in the string using Equation 2.
2) Calculate the predicted wavelength for the fundamental (N = 1) frequency using Equation 3 setting N = 1 for the 1st harmonic (fundamental mode of vibration).
3) Use N = 2, 3, 4, and 5 to calculate the predicted wavelength for each

Answer 1

Without the actual tension value, the wave velocity cannot be calculated. Once the velocity is known, the wavelengths for different harmonics can be determined by applying the formula for the wavelength corresponding to the specific harmonic number, where the wavelength for the fundamental frequency is twice the length of the string.

Step-by-step explanation:

To predict the velocity of waves in the string, you can use the formula v = √(T/μ), where T is the tension in the string and μ is the mass per unit length (linear density). Given that the mass per unit length of the string is 0.004 kg/m, and the tension in the string is not provided, you cannot calculate the wave velocity directly without the tension value.

Once you know the wave velocity, you can then use it to calculate the wavelength for the fundamental frequency (first harmonic) and for higher harmonics by using Equation 3, with N being the respective harmonic number. Remember, the wavelength for the fundamental frequency is twice the length of the string, and for higher harmonics, it will be a fraction of this, determined by the number of the harmonic. For instance, in the first harmonic (N = 1), the wavelength λ is λ = 2L. For the second harmonic (N = 2), the wavelength is λ = L, and so on.