Question

Can someone explain with the Answers pls?

Answer 1

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