A string on a musical instrument (1 m long) carries travelling waves at 100 m/s.

What are the three lowest notes that this string can play (keeping the string at its full length)?

You have the length. You can put one half wavelength on the string, one wavelength, or 3/2 wavelength.

Use the wave equation to determine frequency.

Check my thinking.

What is the wave equation?

The wave equation is a mathematical equation that describes the behavior of waves. It is given by:

v = f * λ

where:
v is the velocity of the wave,
f is the frequency of the wave,
and λ is the wavelength of the wave.

To determine frequency, we need to rearrange the equation to solve for it:

f = v / λ

In this case, we know the velocity of the wave is 100 m/s and we want to find the frequency for different wavelengths.

First, let's calculate the frequency for the case where we put one half wavelength on the string:

λ = (1/2) * 1 m = 0.5 m

f = 100 m/s / 0.5 m = 200 Hz

So, when putting one half wavelength on the string, the frequency is 200 Hz.

Next, let's calculate the frequency for the case where we put one full wavelength on the string:

λ = 1 * 1 m = 1 m

f = 100 m/s / 1 m = 100 Hz

So, when putting one full wavelength on the string, the frequency is 100 Hz.

Finally, let's calculate the frequency for the case where we put three halves wavelength on the string:

λ = (3/2) * 1 m = 1.5 m

f = 100 m/s / 1.5 m = 66.67 Hz

So, when putting three halves wavelength on the string, the frequency is approximately 66.67 Hz.

Therefore, the three lowest notes that this string can play, keeping the string at its full length, are approximately 66.67 Hz, 100 Hz, and 200 Hz.