The fundamental mode of a pipe open at one end and closed at the other (also known as the first harmonic or the fundamental frequency) is when there is a node (point of no displacement) at the closed end and an antinode (point of maximum displacement) at the open end. This forms a standing wave that is essentially half of a wavelength.

Step 1: Identify the length of the pipe and the speed of sound in air. In this case, the length of the pipe (L) is 20 cm or 0.2 m, and the speed of sound (v) is 331 m/s.

Step 2: Since the pipe is closed at one end and open at the other, the length of the pipe is equal to half the wavelength of the fundamental mode. This is because the wave pattern in the pipe for the fundamental frequency is such that it has a node at the closed end and an antinode at the open end, which forms half a wave. Therefore, we can say that L = λ/2.

Step 3: Solve the equation from step 2 for the wavelength (λ). Multiply both sides of the equation by 2 to isolate λ on one side of the equation: λ = 2L.

Step 4: Substitute the given length of the pipe into the equation: λ = 2 * 0.2 m = 0.4 m.

So, the wavelength of the fundamental mode for a 20 cm long organ pipe filled with air, open at one end and closed at the other, at 0°C, is 0.4 m.

Question

The fundamental mode of a pipe open at one end and closed at the other (also known as the first harmonic or the fundamental frequency) is when there is a node (point of no displacement) at the closed end and an antinode (point of maximum displacement) at the open end. This forms a standing wave that is essentially half of a wavelength.

Step 1: Identify the length of the pipe and the speed of sound in air. In this case, the length of the pipe (L) is 20 cm or 0.2 m, and the speed of sound (v) is 331 m/s.

Step 2: Since the pipe is closed at one end and open at the other, the length of the pipe is equal to half the wavelength of the fundamental mode. This is because the wave pattern in the pipe for the fundamental frequency is such that it has a node at the closed end and an antinode at the open end, which forms half a wave. Therefore, we can say that L = λ/2.

Step 3: Solve the equation from step 2 for the wavelength (λ). Multiply both sides of the equation by 2 to isolate λ on one side of the equation: λ = 2L.

Step 4: Substitute the given length of the pipe into the equation: λ = 2 * 0.2 m = 0.4 m.

So, the wavelength of the fundamental mode for a 20 cm long organ pipe filled with air, open at one end and closed at the other, at 0°C, is 0.4 m.

Knowee AI · Accepted Answer

The fundamental mode of a pipe open at one end and closed at the other (also known as the first harmonic or the fundamental frequency) is when there is a node (point of no displacement) at the closed end and an antinode (point of maximum displacement) at the open end. This forms a standing wave that is essentially half of a wavelength.

Step 1: Identify the length of the pipe and the speed of sound in air. In this case, the length of the pipe (L) is 20 cm or 0.2 m, and the speed of sound (v) is 331 m/s.

Step 2: Since the pipe is closed at one end and open at the other, the length of the pipe is equal to half the wavelength of the fundamental mode. This is because the wave pattern in the pipe for the fundamental frequency is such that it has a node at the closed end and an antinode at the open end, which forms half a wave. Therefore, we can say that L = λ/2.

Step 3: Solve the equation from step 2 for the wavelength (λ). Multiply both sides of the equation by 2 to isolate λ on one side of the equation: λ = 2L.

Step 4: Substitute the given length of the pipe into the equation: λ = 2 * 0.2 m = 0.4 m.

So, the wavelength of the fundamental mode for a 20 cm long organ pipe filled with air, open at one end and closed at the other, at 0°C, is 0.4 m.

A 20 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 wavelength of the fundamental mode?

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