Question

A rabid kitten is shrinking loudly, making sound waves a wavelength of 44 cm. What is the sound frequency? What is the period?

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Darrell

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To determine the sound frequency and period, we need to understand the relationship between wavelength, frequency, and period.
- Wavelength (λ) is the distance between two consecutive points in a sound wave that are in phase with each other. In this case, the wavelength is given as 44 cm.
- Frequency (f) is the number of complete cycles or vibrations per second that a sound wave undergoes. It is measured in Hertz (Hz).
- Period (T) is the time it takes for one complete cycle or vibration to occur. It is the reciprocal of the frequency and is measured in seconds (s).
To calculate the frequency, we use the formula:
f = 1 / T
where T is the period. Rearranging the formula, we can express the period as:
T = 1 / f
In this scenario, we are given the wavelength (λ) of 44 cm. To find the frequency, we need to convert the wavelength from centimeters to meters (since SI units are typically used for frequency calculations).
Converting 44 cm to meters, we have:
44 cm = 44 / 100 m = 0.44 m
Now, we can calculate the frequency:
f = speed of sound / λ
The speed of sound in air is approximately 343 meters per second. Plugging in the values:
f = 343 m/s / 0.44 m
Calculating the frequency, we get:
f ≈ 779.5 Hz (rounded to one decimal place)
To find the period, we can use the formula:
T = 1 / f
Plugging in the frequency value:
T ≈ 1 / 779.5 Hz ≈ 0.0013 seconds (rounded to four decimal places)
So, the sound frequency of the rabid kitten is approximately 779.5 Hz, and the corresponding period is approximately 0.0013 seconds.

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