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Orchestra instruments are commonly tuned to match an A-note played by the principal oboe. The Baltimore Symphony Orchestra tunes to an A-note at 440 Hz while the Boston Symphony Orchestra tunes to 442 Hz. If the speed of sound is constant at 343 m/s, find the magnitude of difference between the wavelengths of these two different A-notes. (Enter your answer in m.)

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cjrodriguez89

Answer:

Δλ = 3*10⁻³ m.

Explanation:

  • At any wave, there exists a fixed relationship between the speed of  the wave, the wavelength, and the frequency, as follows:

       [tex]v = \lambda* f (1)[/tex]

       where v is the speed, λ is the wavelength and f is the frequency.

  • Rearranging terms, we can get λ from the other two parameters, as follows:

       [tex]\lambda = \frac{v}{f} (2)[/tex]

  • Since v is constant for sound at 343 m/s, we can find the different wavelengths at different frequencies, as follows:

        [tex]\lambda_{1} =\frac{v}{f_{1}} = \frac{343m/s}{440(1/s)} = 0.779 m (3)[/tex]

        [tex]\lambda_{2} =\frac{v}{f_{2}} = \frac{343m/s}{442(1/s)} = 0.776 m (4)[/tex]

  • The difference between both wavelengths, is just the difference between (3) and (4):

       [tex]\Delta \lambda = \lambda_{1} - \lambda_{2} = 0.779 m - 0.776m = 3e-3 m (5)[/tex]

       ⇒ Δλ = 3*10⁻³ m.

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