QuestionJune 25, 2025

A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0^circ C is 331m/s What is the wavelength of the third mode of vibration? Multiple Choice 30 cm 36 cm 24 cm 12 cm 48 cm

A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0^circ C is 331m/s What is the wavelength of the third mode of vibration? Multiple Choice 30 cm 36 cm 24 cm 12 cm 48 cm
A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0^circ C is 331m/s What is the wavelength of the third mode of vibration? Multiple Choice 30 cm 36 cm 24 cm 12 cm 48 cm

Solution
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Answer

24 cm Explanation 1. Determine the mode of vibration For a pipe open at one end and closed at the other, the third mode corresponds to the fifth harmonic. 2. Calculate the wavelength for the third mode The formula for the wavelength in a pipe closed at one end is \lambda_n = \frac{4L}{n}, where n is an odd integer (harmonic number). For the third mode (fifth harmonic), n = 5. Given L = 30 \text{ cm} = 0.3 \text{ m}, calculate \lambda_5: \[ \lambda_5 = \frac{4 \times 0.3}{5} = \frac{1.2}{5} = 0.24 \text{ m} = 24 \text{ cm} \]

Explanation

1. Determine the mode of vibration<br /> For a pipe open at one end and closed at the other, the third mode corresponds to the fifth harmonic.<br /><br />2. Calculate the wavelength for the third mode<br /> The formula for the wavelength in a pipe closed at one end is $\lambda_n = \frac{4L}{n}$, where $n$ is an odd integer (harmonic number). For the third mode (fifth harmonic), $n = 5$. Given $L = 30 \text{ cm} = 0.3 \text{ m}$, calculate $\lambda_5$:<br />\[<br />\lambda_5 = \frac{4 \times 0.3}{5} = \frac{1.2}{5} = 0.24 \text{ m} = 24 \text{ cm}<br />\]
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