The wings of the blue-throated hummingbird (Lampornis clemenciae), which inhabits Mexico and the southwestern United States, beat at a rate of up to 900 times per minute. Calculate (a) the period of vibration of this bird's wings, (b) the frequency of the wings' vibration, and (c) the angular frequency of the bird's wing beats.

검증된 단계별 안내

To find the period of vibration (T), use the formula T = 1/f, where f is the frequency. First, convert the wing beat rate from beats per minute to beats per second by dividing 900 beats/minute by 60 seconds/minute.

The frequency (f) is the number of wing beats per second. After converting the wing beat rate to beats per second, you have the frequency in Hz (Hertz).

Now, calculate the period (T) using the formula T = 1/f. This will give you the time in seconds for one complete cycle of wing beats.

To find the angular frequency (ω), use the formula ω = 2πf, where f is the frequency in Hz. This will give you the angular frequency in radians per second.

Ensure all units are consistent and check your calculations for accuracy. The period will be in seconds, the frequency in Hz, and the angular frequency in radians per second.

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주요 개념

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Period of Vibration

The period of vibration is the time it takes for one complete cycle of motion. It is the reciprocal of frequency and is measured in seconds. For the hummingbird's wings, the period can be calculated by taking the inverse of the frequency, which is the number of wing beats per second.

Frequency

Frequency refers to the number of complete cycles or vibrations per unit of time, typically measured in hertz (Hz). In this context, it is the number of times the hummingbird's wings beat in one second. To find the frequency, divide the number of beats per minute by 60.

Angular Frequency

Angular frequency is a measure of how quickly an object rotates or oscillates, expressed in radians per second. It is related to the frequency by the formula ω = 2πf, where ω is the angular frequency and f is the frequency. This concept helps describe the rotational aspect of the wing beats.