Question

the tension in a particular piano string is 1067n . when struck or plucked, the resulting wave on the string has a period of 0.660 ms and a wavelength of 0.940 m. ≈50% Part (a) What is the linear mass density, μ, in kilograms per meter, of the string? μ=3.154 kg/mX Incorrect!

Answer 1

The linear mass density of the piano string is calculated to be approximately 0.000525 kg/m using the wave equation that relates wave speed, tension, and linear mass density.

Step-by-step explanation:

To calculate the linear mass density (μ) of a piano string, we can make use of the wave equation that relates the wave speed (v), tension (T), and linear mass density (μ) to each other: v=√(T/μ). From the given information, we know the tension (T) is 1067 N and the wave has a wavelength (λ) of 0.940 m. The period (T) of the wave is 0.660 ms, which is 0.000660 seconds. First, we need to convert the period into frequency (f) as f = 1/T, then apply it in the wave speed formula v = fλ. After obtaining the wave speed, we solve for μ using μ = T/v².

Using these steps:

• Calculate the frequency, f = 1/period = 1/0.000660 s = 1515.15 Hz
• Calculate the wave speed, v = wavelength × frequency = 0.940 m × 1515.15 Hz = 1424.24 m/s
• Solve for μ, μ = T/v² = 1067 N / (1424.24 m/s)² ≈ 0.000525 kg/m

The calculated linear mass density of the piano string is approximately 0.000525 kg/m.