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0° C sound wave travels at 330 m/s in air. A distant horn is producing a note that has a frequency of 440 Hz. How long would that sound wave be? How long does it take a complete wave to pass you by? (That is, what's its period?)

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Final answer:

The length of the sound wave produced by the distant horn would be 0.75 meters and the period of the wave would be approximately 0.0023 seconds.

Step-by-step explanation:

To calculate the length of a sound wave, we need to use the formula:

speed = frequency × wavelength

Given that the speed of sound in air is 330 m/s and the frequency of the note produced by the horn is 440 Hz, we can rearrange the formula to solve for wavelength:

wavelength = speed / frequency

Substituting the given values, we get:

wavelength = 330 m/s / 440 Hz = 0.75 m

Therefore, the length of the sound wave would be 0.75 meters.

To calculate the period of the sound wave, we can use the formula:

period = 1 / frequency

Substituting the given frequency of 440 Hz, we get:

period = 1 / 440 Hz = 0.0023 seconds

The question is about calculating the wavelength and period of a sound wave using its frequency and the speed of sound. Since the sound wave travels at 330 m/s in air, and the distant horn is producing a sound with a frequency of 440 Hz, the wavelength (λ) can be found using the formula λ = v/f, where 'v' is the speed of sound and 'f' is the frequency. Substituting the given values: λ = 330 m/s / 440 Hz = 0.75 meters. This is the length of the sound wave. The time it takes for a complete wave to pass, known as its period (T), can be calculated using the formula T = 1/f. Thus, T = 1/440 Hz = 0.002273 seconds (approx.). This is the period of the sound wave.

Therefore, it would take approximately 0.0023 seconds for a complete wave to pass by you.

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