Sound Waves Legacy Problem #31 Guided Solution
Problem*
South's orchestra walk on stage, take their seats and attempt to tune all instruments to 440 Hz - the A note of the oboe. Elizabeth tunes the A-string of her violin to the oboe. At one point in the process, she detects beats of 2 Hz between her string and the oboe. If her string is playing too low of a pitch, then what is its frequency?
Audio Guided Solution
When two sound waves with slightly different frequencies are played simultaneously, an observer will hear beats. Beats result from these two sounds of slightly different frequencies in their herd as periodic and repeating fluctuations in the loudness of the sound. The orchestra uses beats in order to tune their instruments to one another. So the violin needs to be tuned to all the other instruments and typically how it's done is everyone tunes their instrument to the oboe. So the oboe is played and all the other members of the orchestra listen to the sound of the oboe and begin to tune their instrument until it matches the frequency of the oboe. As it begins to get close to the frequency of the oboe, they'll begin to hear beats, periodic and repeating fluctuations in the amplitude or loudness of their sound anyway. Now beats are always characterized by a beat frequency, which describes how frequently this periodic fluctuation in intensity or loudness occurs. So a beat frequency of two hertz always indicates to a member of the orchestra that their instrument is two hertz different in frequency than the frequency of the oboe. So if Elizabeth is hearing a two hertz beat, she knows that the frequency of her instrument is either 442 hertz or 438 hertz. So now she just listens a little more carefully to see if the sound of her instrument is higher in pitch or lower in pitch than the oboe. And if she notices that it's lower in pitch, then what she knows is her frequency of her string is 438 hertz.
Solution
438 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!
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