A note was played on a a keyboard. The frequency of the note was 440 Hz. (a) What does a frequency of 440 Hz mean? (b) The sound waves produced by the keyboard travel at a speed of 340 m/s. Calculate the wavelength of the note.
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(a) A frequency of 440 Hz means that a single trough and peak of the sound wave oscillates 440 times per second or equally that 440 sound waves are produced by the keyboard per second (This is because the SI unit of a Hz is inverse seconds s^-1)
(b) We first need the equation that relates the two given quantities we have (wave velocity and frequency) to the third unknown, desired quantity (wavelength). This is equation is a simple one, v = f lambda. We want the quantity lambda, so we have to divide both sides of the equation by f to get v / f = lambda. We then plug in the numbers to find lambda, the wavelength, which is lambda = 340 m /s / 440 /s = 340/440 m (as the /s units cancel out leaving just length which is the correct unit for a wavelength!)
