The G string of a violin is a little too tightly stretched. Five beats per secon

Question

The G string of a violin is a little too tightly stretched. Five beats per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at 196 Hz at equal loudness a.) What is the period of the violin string's oscillation? b.) What is the observed musical note when these two notes play together? C.) Suppose you generate the same two notes (from violin string and tuning fork) on a computer, where you can simplify the scenario-- making sure their individual amplitudes are the same (5 nm) and that they have n phase offset take both to be zero when they exit a speaker x 0) Complete the equation below for the resultant sound wave that will leave the speaker in the +x direction nm) sin( 1 x- : rad·s-1 t) . cos( rad s t) TRY IT HERE!

Explanation / Answer

(a) Let the period be T.
Then the beat frequency [1/T - 196Hz] = 5 beats s-1.
T = 4.97 × 10–3s= 5ms
(b) f = 1/T
f = 1/[4.97 × 10–3s]
f = 201 Hz
The string that is “too tightly stretched” has the higher tension and thus the higher (fundamental) frequency.
Alternative solution: f - 196 Hz = 5 beats s-1
f = 201 Hz

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