# Inferring Relationships On a piano keyboard, the CS key has a frequency that is twice the frequency of the middle C key. Is the string that vibrates to make the sound waves for the CS key shorter or longer than the middle C string? Explain your reasoning.

Inferring Relationships On a piano keyboard, the CS key has a frequency that is twice the frequency of the middle C key. Is the string that vibrates to make the sound waves for the CS key shorter or longer than the middle C string? Explain your reasoning.
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LitikoIDu6
In this question, we are given that the C5 key in a piano has a frequency that is double of that of the C key. Our task is determine whether the string associated with the C5 key is shorter or longer than that of the C string.
The frequency f of a string is inversely proportional to the length l of the string.
Since the frequency of the C5 key is twice of that of the C key, then the C5 string must be shorter than the C string.
Result:
Shorter.