(a) Greater
The frequency of the nth-harmonic on a string is an integer multiple of the fundamental frequency, :
So we have:
- On wire A, the second-harmonic has frequency of , so the fundamental frequency is:
- On wire B, the third-harmonic has frequency of , so the fundamental frequency is
So, the fundamental frequency of wire A is greater than the fundamental frequency of wire B.
(b)
For standing waves on a string, the fundamental frequency is given by the formula:
where
v is the speed at which the waves travel back and forth on the wire
L is the length of the string
(c) Greater speed on wire A
We can solve the formula of the fundamental frequency for v, the speed of the wave:
We know that the two wires have same length L. For wire A, , while for wave B,
, so we can write the ratio between the speeds of the waves in the two wires:
So, the waves travel faster on wire A.