A constrained string with a length of 8.5 meters is vibrating at its fundamental frequency of 113.1 Hz. What is the frequency of the 7th harmonic on this string?

The fundamental (first harmonic) wavelength is 17.0 meters.

Second harmonic: 8.5 m
Third harmonic: 5.67 m
Sixth harmonic: 2.83 m
Seventh harmonic: 2.429 m

Frequency*wavelength = constant
= 1923 m/s
Seventh harmonic frequency = 792 Hz

To find the frequency of the 7th harmonic on a constrained string, we need to understand the relationship between the fundamental frequency and harmonic frequencies.

The fundamental frequency, represented as f₁, is the frequency at which the entire string vibrates in one complete cycle. Harmonics, represented as fₙ (where n is the harmonic number), are integer multiples of the fundamental frequency.

The relationship between the fundamental and the harmonic frequencies is given by the formula:

fₙ = nf₁

In this case, we know the fundamental frequency (f₁) is 113.1 Hz, and we need to find the frequency of the 7th harmonic (f₇).

Using the formula, we can substitute the values:

f₇ = 7 * f₁

So, to find the frequency of the 7th harmonic, we multiply the fundamental frequency by 7.

Let's calculate it:

f₇ = 7 * 113.1 Hz

f₇ = 791.7 Hz

Therefore, the frequency of the 7th harmonic on this string is 791.7 Hz.