The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (a) What is the wavelength of such a sound wave?

검증된 단계별 안내

Step 1: Understand the problem. We are asked to find the wavelength of a sound wave. We know the speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz.

Step 2: Recall the formula that relates the speed of a wave (v), its frequency (f), and its wavelength (λ). This formula is v = f * λ.

Step 3: Rearrange the formula to solve for the wavelength. This gives us λ = v / f.

Step 4: Substitute the given values into the formula. The speed of sound (v) is 343 m/s and the frequency (f) is 20 Hz.

Step 5: Calculate the wavelength (λ) by dividing the speed of sound by the frequency. This will give you the wavelength of the sound wave in meters.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Wave Speed

Wave speed is the distance traveled by a wave per unit of time. In the context of sound waves, it is determined by the medium through which the sound is traveling. For dry air at 20 °C, the speed of sound is approximately 343 m/s. Understanding wave speed is essential for calculating other properties of sound waves, such as wavelength and frequency.

Frequency

Frequency is the number of cycles of a wave that pass a given point per unit of time, typically measured in hertz (Hz). In this case, the lowest frequency sound wave detectable by the human ear is about 20 Hz. Frequency is inversely related to wavelength; as frequency increases, wavelength decreases, and vice versa, which is crucial for solving the problem.

Wavelength

Wavelength is the distance between successive crests (or troughs) of a wave. It is related to wave speed and frequency through the equation: wavelength = wave speed / frequency. For sound waves, knowing the wavelength helps in understanding how sound interacts with the environment, including phenomena like resonance and sound quality.