The lower A on a piano has a frequency of 27.5 Hz.If the tension in the 2.0-m-long string is 304 N and one-half wavelength occupies the string,what is the mass of the string?
A)100 g
B)25 g
C)37 g
D)50 g

Question

Quizplus · Accepted Answer

The wave speed v on the string is given by v = fλ, where f is the frequency and λ is the wavelength. Since one-half wavelength occupies the string, λ = 2 * 2.0 m = 4.0 m. Thus, v = 27.5 Hz * 4.0 m = 110 m/s. The wave speed is also given by v = sqrt(T/μ), where T is the tension and μ is the mass per unit length. Solving for μ gives μ = T/v^2 = 304 N / (110 m/s)^2 = 0.0252 kg/m. The total mass m of the string is μ * length = 0.0252 kg/m * 2.0 m = 0.0504 kg, or approximately 50 g.

The Lower a on a Piano Has a Frequency of 27.5