the lowest note emitted by stretched string has a frequency of 40 Hz. how many overtones are there between 40 Hz and 180 Hz. please answer this with solvings and explanation?

All_for_one

2 years ago

To find the number of overtones between 40 Hz and 180 Hz, we can use the formula for the frequencies of overtones in a stretched string, which is given by:

\[ f_n = nf_1 \]

Where:
- \( f_n \) = frequency of the nth overtone
- \( f_1 \) = frequency of the fundamental (lowest) note
- \( n \) = overtone number

First, let's find the frequency of the second overtone (n=2):
\[ f_2 = 2 \times 40 \]
\[ f_2 = 80 \, \text{Hz} \]

Next, let's find the frequency of the third overtone (n=3):
\[ f_3 = 3 \times 40 \]
\[ f_3 = 120 \, \text{Hz} \]

Finally, let's find the frequency of the fourth overtone (n=4):
\[ f_4 = 4 \times 40 \]
\[ f_4 = 160 \, \text{Hz} \]

Now, we can see that there are three overtones between 40 Hz and 180 Hz, which are the second, third, and fourth overtones.

Therefore, there are 3 overtones between 40 Hz and 180 Hz.

I hope this helps!