Answer
The frequencies of the other three forks are $501~Hz, 503~Hz,$ and $508~Hz$
The frequencies of the other three forks are $505~Hz, 507~Hz,$ and $508~Hz$
Work Step by Step
Set 1:
The lowest frequency is $500~Hz$
To produce a beat frequency of $8~Hz$, the highest frequency must be $508~Hz$
To produce a beat frequency of $1~Hz$ and $7~Hz$, we could include a frequency of $501~Hz$
To produce a beat frequency of $2~Hz, 3~Hz,$ and $5~Hz$, we could include a frequency of $503~Hz$
The frequencies of the other three forks are $501~Hz, 503~Hz,$ and $508~Hz$
Set 2:
The lowest frequency is $500~Hz$
To produce a beat frequency of $8~Hz$, the highest frequency must be $508~Hz$
To produce a beat frequency of $1~Hz$ and $7~Hz$, we could include a frequency of $507~Hz$
To produce a beat frequency of $2~Hz, 3~Hz,$ and $5~Hz$, we could include a frequency of $505~Hz$
The frequencies of the other three forks are $505~Hz, 507~Hz,$ and $508~Hz$
