A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning fork of frequency 440 Hz. She hears a beat frequency of 4 Hz. She notices that, when she increases the tension in the string slightly, the beat frequency decreases. What was the frequency of the mistuned A string?

Question

Physics

Zackery Rich

16 December, 06:12

A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning fork of frequency 440 Hz. She hears a beat frequency of 4 Hz. She notices that, when she increases the tension in the string slightly, the beat frequency decreases. What was the frequency of the mistuned A string?

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Answers (1)

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Cailyn · Answer 1

f_2 = 436 Hz

Explanation:

Given:

- Frequency of the note played f_1 = 440 Hz

- Number of beats heard per second b = 4 Hz

Find:

What was the frequency of the mis-tuned A string?

Solution:

- The beat is the difference in frequency of the notes played and is given by the expression:

| f_1 - f_2 | = beats

- we heard 4 beats, so

| f_1 - f_2 | = 4

- Plug in the value: | 440 - f_2 | = 4

Hence, f_2 = 436 Hz