Final answer:
The period of one vibration for a low A note with a frequency of 27.5 Hz is approximately 0.0364 seconds. For a piano where one string is tuned to 260 Hz and beats of 1.5 Hz are produced, the other string could be tuned to either 261.5 Hz or 258.5 Hz.
Step-by-step explanation:
To find the period of one vibration of the low A note with a frequency of 27.5 Hz, we use the relationship between period (T) and frequency (f), which is T = 1/f. Now substituting the frequency into the formula, we get T = 1/27.5 Hz. Therefore, the period of the note is approximately 0.0364 seconds, which is the amount of time it takes for one complete vibration cycle of that particular sound wave.
Now, addressing the issue with the piano, when the middle C hammer of a piano hits two strings producing beats of 1.50 Hz with one of the strings tuned to 260.00 Hz, the other string could have frequencies of either 261.50 Hz or 258.50 Hz. This is because beats occur when two sound waves of similar but not identical frequencies interfere with each other, the beat frequency is the absolute difference between the two frequencies. Therefore, the second string could be slightly higher (260 Hz + 1.5 Hz) or slightly lower (260 Hz - 1.5 Hz) than the first string.