What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.
A)517 Hz
B)234 Hz
C)181 Hz
D)312 Hz
E)366 Hz

Question

Quizplus · Accepted Answer

We can use the formula for the fundamental frequency of a string:
f = (1/2L) √(T/μ)

Where:
L = length of the wire
T = tension in the wire
μ = linear density of the wire (mass per unit length)

First, we need to convert the mass of the wire from grams to kilograms:
m = 5.60 g = 0.0056 kg

Then, we can plug in the values and solve for f:

f = (1/2 x 0.600 m) √(440 N / (0.0056 kg/m))
f = 0.181 kHz = 181 Hz

Therefore, the answer is C) 181 Hz.

What Is the Frequency of the Fundamental Mode of Vibration