A 30 hz sound is annoying or dissonant to the ear. If one clarinet plays a sound at a frequency of 360 Hz, at what frequencies (more than one) might another clarinet simultaneously play so that dissonant 30 Hz beats are created? Explain.
F1 = 360 - 30 = 330 Hz. = The diff.freq
F2 = 360 + 30 = 390 Hz. = The sum freq
To determine the frequencies at which another clarinet might simultaneously play to create dissonant 30 Hz beats with the first clarinet, we need to understand the concept of beat frequencies.
Beat frequencies are the result of two sound waves interfering with each other when their frequencies are slightly different. The interference creates periodic variations in the loudness of the combined sound, known as beats.
In this case, to create dissonant 30 Hz beats, we need the beat frequency to be 30 Hz. The beat frequency is calculated by subtracting the frequency of one sound wave from the frequency of the other sound wave. So, we need to find two numbers whose difference is 30 Hz.
To find the frequencies, we can set up an equation:
f1 - f2 = 30 Hz,
where f1 is the frequency of the first clarinet (360 Hz) and f2 is the frequency of the second clarinet.
Now, we can substitute the known values and solve for f2:
360 Hz - f2 = 30 Hz,
Rearranging the equation:
f2 = 360 Hz - 30 Hz = 330 Hz.
Therefore, to create dissonant 30 Hz beats, the second clarinet could play at a frequency of 330 Hz while the first clarinet plays at a frequency of 360 Hz.