A stretched string has a third harmonic frequency of 600 Hz. What is the frequency of the second harmonic?
The wavelength of the third harmonic will be 2/3 of the wavelength of the second harmonic.
Since frequency is inversely proportional to wavelength for standing waves, the frequency is higher by a factor 3/2.
To find the frequency of the second harmonic, we first need to understand what harmonics are. Harmonics are multiples of the fundamental frequency of a vibrating system. The fundamental frequency is the lowest frequency at which an object can vibrate or resonate.
In this case, the third harmonic frequency is given as 600 Hz. This means that the frequency of the third harmonic is three times the frequency of the fundamental frequency. So, we can write an equation to find the fundamental frequency as follows:
Fundamental frequency = Third harmonic frequency / Number of Harmonics
Plugging in the values, we get:
Fundamental frequency = 600 Hz / 3 = 200 Hz
Now that we know the fundamental frequency is 200 Hz, we can find the frequency of the second harmonic by multiplying the fundamental frequency by 2. Therefore, the frequency of the second harmonic is:
Second harmonic frequency = Fundamental frequency * 2 = 200 Hz * 2 = 400 Hz
Therefore, the frequency of the second harmonic is 400 Hz.