Explain what beats are and why they occur…

1) When two sounds are slightly different in frequency, a “warbling” beat is heard

2) This is because the two waves are in phase for a while, so constructively interfere to produce a large amplitude (loud) sound wave

3) Then they then drift out of phase, so destructively interfere to produce a small amplitude (quiet) sound wave.

4) Eventually they return back in phase again and the resulting sound will fluctuate as the net volume increases and decreases with a frequency given by:

fbeat = f1 – f2

A tuning fork labelled “middle C, 256Hz” is used to tune a piano string. Four beats are heard every second. The tension in the string is increased until the beats disappear.

What was the frequency of the note produced by the string before it was tuned?

Do now:Wednesday, April 19, 2023

fbeat = f1 – f2

“Four beats are heard every second” means: fbeat = 4Hz

So piano could be either 256 + 4 = 260Hz

or 256 – 4 = 252Hz (A)

“The tension in the string is increased until the beats disappear” means:•As the tension is increased, the wave speed increases•But the wavelength must stay the same because the length of the piano string has not changed •So using v = f λ, this means f must have increased•So the piano was originally at 252 Hz (E)

Tasks:

1)Activity 5A should already be finished

2)Finish Activity 5B today