The speed of sound in dry air at is 343 m/s, and the middle C on a piano keyboard has a frequency of 261 Hz. a. What is the wavelength of the sound wave corresponding to a middle C?

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Identify the formula to calculate the wavelength of a sound wave: \( \lambda = \frac{v}{f} \), where \( \lambda \) is the wavelength, \( v \) is the speed of sound, and \( f \) is the frequency.

Substitute the given values into the formula: \( v = 343 \text{ m/s} \) and \( f = 261 \text{ Hz} \).

Perform the division to find the wavelength: \( \lambda = \frac{343}{261} \).

Simplify the expression to find the wavelength in meters.

Ensure the units are consistent and the final answer is in meters, as the speed of sound is given in meters per second.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wave Speed Formula

The speed of a wave is determined by the formula v = fλ, where v is the wave speed, f is the frequency, and λ (lambda) is the wavelength. This relationship shows that the speed of sound in a medium is constant, and the wavelength can be calculated if the frequency is known.

Frequency

Frequency refers to the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). In this context, the frequency of middle C is 261 Hz, meaning 261 sound wave cycles occur every second, which directly influences the wavelength of the sound produced.

Wavelength

Wavelength is the distance between successive crests (or troughs) of a wave, typically measured in meters. It is inversely related to frequency; as frequency increases, wavelength decreases. For sound waves, understanding wavelength is crucial for applications in acoustics and music.

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Textbook Question

The speed of sound in dry air at is 343 m/s, and the middle C on a piano keyboard has a frequency of 261 Hz. b. What would be the frequency of electromagnetic radiation with the same wavelength?

Textbook Question

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation.

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Textbook Question

A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (b) Would the radiation produced by the appliance be visible to the human eye?

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