The A string of a violin is a little too tightly stretched. Beats at 6 per second are heard when the string is sounded together with a tuning fork oscillating accurately at concert A. What is the period of the violin string oscillations?

Question

27-10-2023
Physics

High School

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The A string of a violin is a little too tightly stretched. Beats at 6 per second are heard when the string is sounded together with a tuning fork oscillating accurately at concert A. What is the period of the violin string oscillations?

Answer :

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Anastasia2022 Anastasia2022 · Answer 1 · 2024-10-14T22:27:28-04:00

The period of the violin string oscillations is 0.0022 seconds.

The beat frequency of 6 per second means that the frequency of the violin string oscillations is slightly higher than the frequency of the tuning fork.

We can use the formula for beat frequency to find the difference in frequency between the two:

Beat frequency = |f1 - f2|

where f1 and f2 are the frequencies of the two sources.

In this case, the beat frequency is 6 beats per second and the frequency of the tuning fork is the standard Concert A pitch of 440 Hz. So we have:

6 = |f1 - 440|

Solving for f1, we get:

f1 = 446 Hz or 434 Hz

The two possible frequencies of the violin string are 446 Hz and 434 Hz, with 440 Hz being the frequency of the tuning fork.

The period of a wave is the time it takes for one complete oscillation or cycle. It can be calculated as:

period = 1 / frequency

So the period of the violin string oscillations for a frequency of 446 Hz would be:

period = 1 / 446 Hz ≈ 0.0022 seconds

And for a frequency of 434 Hz:

period = 1 / 434 Hz ≈ 0.0023 seconds