Question

The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440Hz).What is the period of the violin string oscillation?

Short answer

The period of the violin string oscillation is$2.25\times {10}^{-3}s$.

Step-by-step solution

The given data

1. Frequency of the violin, f₂ = 440Hz
2. Beat frequency is, f = 4beats/s.

Understanding the concept of frequency

We can find the frequency of the violin using the formula for beat frequency. Then using the relation between period and frequency, we can find the period of the violin string oscillation.

Formula:

The period of an oscillation,

$\mathit{T}\mathbf{=}\frac{\mathbf{1}}{\mathbf{f}}$ …(1)

Calculation of the period of string oscillation

From the above given data,

Beat frequency is expressed as,

$f=f_1-f_2$

Substitute all the value in the above equation.

4beats/s = f₁-440Hz

f₁ = 444Hz

Now, the period of the violin string oscillation is given using equation (1) as:

role="math" localid="1661424941161" $\begin{array}{rcl}T& =& \frac{1}{444Hz}\\ & =& 0.005525s\\ & =& 2.25\times {10}^{-3}s\end{array}$

Hence, the value of period is $\begin{array}{rcl}& & 2.25\times {10}^{-3}s\end{array}$.