A 572-Hz longitudinal wave in air has a speed of 345 m/s. At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?

검증된 단계별 안내

Determine the wavelength of the wave using the formula:

λ = \frac{v}{f}

, where

v

is the speed of the wave (345 m/s) and

f

is the frequency (572 Hz).

Convert the distance between the two points (4.4 cm) into meters by dividing by 100, since 1 cm = 0.01 m.

Calculate the fraction of the wavelength that corresponds to the distance between the two points using the formula:

fraction = \frac{d}{λ}

, where

d

is the distance (in meters) and

λ

is the wavelength.

Convert the fraction of the wavelength into a phase difference in degrees using the formula:

phase = \frac{fraction \times 360}{1}

, since one full wavelength corresponds to 360 degrees.

Express the phase difference as the final result, ensuring it is within the range of 0 to 360 degrees (if necessary, subtract multiples of 360 to bring it into this range).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Wave Speed

Wave speed is the distance a wave travels per unit of time. In this case, the speed of the longitudinal wave in air is given as 345 m/s. This speed is crucial for determining how quickly the wave propagates through the medium and is essential for calculating the phase difference between two points.

Wavelength

Wavelength is the distance between successive points of similar phase in a wave, such as crest to crest or trough to trough. It can be calculated using the formula λ = v/f, where v is the wave speed and f is the frequency. For the given wave, the wavelength can be determined, which is necessary for finding the phase difference over a specified distance.

Phase Difference

Phase difference refers to the difference in the phase of two points in a wave, typically measured in degrees or radians. It indicates how far one point is ahead or behind another in the wave cycle. The phase difference can be calculated using the formula Δφ = (2π/λ) * Δx, where Δx is the distance between the two points, allowing us to find the phase difference for the specified distance of 4.4 cm.