Piano Problem :)
Classical Mechanics
Level
2
The A key above "Middle C" on the piano produces a sound wave with a frequency of 440 Hz. The speed of sound in air at room temperature is 344 m/s. What is the wavelength of the sound waves associated with middle C?
0.97
1.67
0.78
1.56
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1 solution
The sound wave produced by striking the middle C key on a piano has a frequency of 440 Hz. From the relation : Wave speed = wavelength x frequency,
we can solve for the wavelength of the sound wave, since we know the wave speed is the speed of sound in air (344 m/s). wavelength = wavespeed / frequency, or, wavelength = 344 m/s / 440 Hz = 0.78 m
Note, the sound wave produced from striking the C key one octave higher than middle C has a frequency of 880 Hz. This sound wave has exactly the same wave speed (344 m/s). It's wavelength is half as large (0.39 m) as the sound wave produced by striking the middle C key. Sound waves an octave lower in frequency (220 Hz) would have twice the wavelength (1.56 m).