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in Science & Mathematics by (480 points)

A string (mass 4.7 g, length 2.96 m, and tension 73.8 N), fixed at both ends, vibrates in its second (n = 2) natural mode. What is the wavelength in air of the sound emitted by this vibrating string? The speed of sound in air is 340 m/s. Answer in units of m.

I've tried it and got it wrong. Could someone please help me out?

1 Answer

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by (17.0m points)

λ = vs / f

where

f = v / L

v = √(T / μ)

then

f = √(T / μ) / L

replacing into the first equation on get

λ = L v / √(T / μ) = 4 L v √(μ / T)

where

μ = m / L

then

λ = v √ (m L / T)

λ = 340 * √(4.7x10^-3 * 2.96 / 73.8) = 4.67 m

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