Question

Bob creates an instrument that is able to play C4 (261.63 Hz). He does some analysis with the sound equipment and it shows that when he plays it, he also gets the frequencies 523.26 Hz, 784.89 Hz, and 1308.15 Hz. What could be true about the instrument? It’s a stringed instrument, it’s a closed pipe, or it’s an open pipe?

Answer 1

It could be a stringed instrument or an open pipe.

Step-by-step explanation:

Let v be the speed of sound, y be wavelength and f be frequency.

v = yf

f= v/y; v is constant.

In a stringed instrument, the fundamental frequency note is heard when the length of the string, l = y/2; y= 2l

f′= v/2l

The second harmonic is heard when l= y

f"= v/y

...

f'''= 3v/2l

We can infer that f"= 2f'

f'''= 3f'

This is similar to the values in the question as;

523.26 =2(261.63) and so on.

Same thing happens with open pipes.