A 20.0 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°C is 331 m/s. What is the frequency of the fundamental mode?
Question
A 20.0 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°C is 331 m/s. What is the frequency of the fundamental mode?
Solution
Sure, here are the steps to solve this problem:
Step 1: Understand the problem The organ pipe is open at one end and closed at the other, which means it's a pipe of the first harmonic or fundamental frequency. The length of the pipe is given as 20.0 cm or 0.2 m. The speed of sound in air at 0°C is given as 331 m/s. We need to find the frequency of the fundamental mode.
Step 2: Use the formula for the fundamental frequency The formula for the fundamental frequency (f) of a pipe open at one end and closed at the other is given by:
f = v / 4L
where: v = speed of sound in air L = length of the pipe
Step 3: Substitute the given values into the formula Substitute v = 331 m/s and L = 0.2 m into the formula:
f = 331 / (4 * 0.2) = 331 / 0.8 = 413.75 Hz
So, the frequency of the fundamental mode is approximately 414 Hz.
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