SEQUENCE of questions:

1)A typical steel B-string in a guitar resonates at its fundamental frequency at 240 Hertz. The length of the string is 0.620 m. What is the wave velocity along the string? Find your answer in m/s
MY ANSWER 148.8m/s?

2)The tension in the above string is 84.0 N. Calculate the mass of a 3 m long piece of the steel string. Find your answer in kilograms

3)Find the wavelength of the third harmonic of the guitar string described in the problem before last.

To answer these questions, we need to use the formulas related to wave velocity, tension, frequency, length, mass, and harmonics.

1) To find the wave velocity along the string, we can use the formula:

Wave velocity (v) = Frequency (f) x Wavelength (λ)

Given that the fundamental frequency is 240 Hz, we can find the wavelength using the formula:

λ = 2 x Length

Substituting the values, we get:

λ = 2 x 0.620 m = 1.240 m

Now, substituting the frequency and wavelength into the wave velocity formula, we have:

v = 240 Hz x 1.240 m = 297.6 m/s

So the wave velocity is 297.6 m/s, not 148.8 m/s as stated in your answer.

2) To find the mass of the string, we can use the formula:

Mass (m) = (Tension (F)) / (Wave velocity (v))^2 x Length (L)

Given that the tension is 84.0 N and the length is 3 m, and using the wave velocity we found in the previous question (297.6 m/s), we can calculate the mass as follows:

m = 84.0 N / (297.6 m/s)^2 x 3 m = 3.17 kg

So the mass of the 3 m long piece of the steel string is 3.17 kg.

3) Finally, to find the wavelength of the third harmonic, we need to use the relationship between the harmonic number (n) and the wavelength. For the third harmonic, the wavelength is given by:

λ = (2 / n) x Length

In this case, the harmonic number is 3, and the length is 0.620 m. Substituting these values, we get:

λ = (2 / 3) x 0.620 m = 0.413 m

So the wavelength of the third harmonic of the guitar string is 0.413 m.