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Answer :
Final answer:
To calculate the first overtone in an ear canal that resonates like a 2.40-cm-long tube closed at one end, we need to determine the wavelength and frequency of this overtone. The frequency of the first overtone in the ear canal is approximately 3681.67 Hz. Whether the ear is particularly sensitive to this frequency depends on individual factors and the context in which the frequency is encountered.
Explanation:
To calculate the first overtone in an ear canal that resonates like a 2.40-cm-long tube closed at one end, we need to determine the wavelength and frequency of this overtone. For a closed tube, the length of the tube determines the wavelength. In this case, the length of the tube is 2.40 cm. To find the wavelength, we can use the formula: wavelength = 4 times the length of the tube. Therefore, wavelength = 4 times 2.40 cm = 9.60 cm.
Next, we can use the formula speed of sound = frequency times wavelength to find the frequency. The speed of sound in air at the given temperature can be approximated as 331.4 m/s + (0.6 m/s/ºC) * temperature in ºC. Plugging in the values, the speed of sound = (331.4 + (0.6 * 37)) m/s ≈ 354.2 m/s.
Finally, we can rearrange the formula to solve for frequency: frequency = speed of sound / wavelength. Plugging in the values, the frequency = 354.2 m/s / (9.60 cm × 0.01 m/cm) ≈ 3681.67 Hz. This is the frequency of the first overtone in the ear canal. As for whether the ear is particularly sensitive to this frequency, it depends on individual factors and the context in which the frequency is encountered.
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