Answer:
a) The frequency of the third harmonic is 786 Hz
b) The frequency of the first harmonic is 340 Hz
c) The frequency of the fifth harmonic is 1640 Hz
Explanation:
The rule is as follows:
If the first harmonic frequency (also called the fundamental frequency) is F, then:
The frequency of the second harmonic (also called the second overtone) is:
2*F
The frequency of the third harmonic (also called the third overtone) is:
3*F
And so on.
With this information, we can answer the questions:
a) We want to find the frequency of the third harmonic, such that the frequency of the first harmonic is 262 Hz.
Then we have F = 262Hz
And the frequency of the third harmonic will be:
3*F = 3*262Hz = 786 Hz
b) First harmonic for a string whose fifth harmonic frequency is 1700Hz.
Let's define F as the first frequency (the one we want to find)
Then the fifth harmonic frequency can be written as:
5*F = 1700Hz
With this equation we can find the value of F:
F = 1700Hz/5 = 340Hz
c) We want to find the fifth harmonic for a string whose third overtone (this is the same as the third harmonic) frequency is 984 Hz.
Then if the frequency of the first harmonic is F, we know that:
3*F = 984 Hz
With this we can find the value of F:
F = 984 Hz/3 =328 Hz
Now that we know the frequency of the first harmonic, we can find the frequency of the fifth harmonic:
5*F = 5*328 Hz = 1640 Hz
