Sound Waves Legacy Problem #32 Guided Solution
Problem*
Marc is attempting to tune his guitar. After adjusting his E4 string to 330 Hz, he begins to tackle the B3 string. In the process, he plucks both strings simultaneously and notices beats occurring at a rate of 12 beats in 4 seconds. When plucked individually, Marc observes the B3 string to sound out at a higher pitch. What is the frequency of the B3 string?
Audio Guided Solution
When two sounds of slightly different frequency are played simultaneously, an observer often hears beats. Beats are the periodic and repeating fluctuations which are heard in the loudness of the sounds, resulting from the interference of the two sound waves. Beats are characterized by a beat frequency. A beat frequency simply indicates how frequently the amplitude or loudness of the sound goes up and down. If you hear 12 beats in 4 seconds, then you're hearing a beat frequency of 3 Hz. So here Mark is trying to tune his guitar and he notices two strings have a 3 Hz difference in frequency. If one of them is playing 330 Hz, then the other one either has to be playing 327 Hz or 333 Hz. Mark notices that the string he's trying to tune is actually a little higher than the string he knows the frequency on. And so if it's 3 Hz higher, it must be playing out at 333 Hz.
Solution
333 Hz
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = 345\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 1.28 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Sound Waves at The Physics Classroom Tutorial.