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A sound of 550 Hz travels from air through a concrete wall. If the speed of sound in air is 340 m/s and the speed of sound in concrete is 3700 m/s, what is the change in wavelength of the sound?

Answer :

Final answer:

When a sound moves from air to concrete, the change in its wavelength is about 6.1091 meters, calculated using the relation between the speed of sound, frequency, and wavelength.

Explanation:

The change in the wavelength of sound when it travels from one medium to another is determined by the change in the speed of sound and the frequency, which remains constant. The speed of sound in air is 340 m/s and in concrete is 3700 m/s, while the frequency is 550 Hz.

The wavelength (λ) in each medium can be calculated using the formula Vw =fλ, where Vw is the speed of sound. Thus, in air, λ (air) = Vw (air) / f = 340 m/s / 550 Hz = 0.61818 m and in concrete, λ (concrete) = Vw (concrete) / f = 3700 m/s / 550 Hz = 6.7273 m. Hence, the change in wavelength is λ (concrete) - λ (air) = 6.7273 m - 0.61818 m = 6.1091 m. Therefore, the change in wavelength of the sound as it moves from air through the concrete wall is approximately 6.1091 meters.

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