Question

an organ pipe is tuned to exactly 384 hz when the temperature in the room is 20c. later, when the air has warmed up to 25c, the frequency is

Answer 1

The frequency of an organ pipe changes with temperature because the speed of sound increases with temperature. A rise in temperature will result in a proportional increase in the frequency of sound produced by the organ pipe.

Step-by-step explanation:

The question deals with how the frequency of sound produced by an organ pipe changes with temperature. In general, the speed of sound in air increases as the temperature increases. This is because the speed of sound in air is given by the formula v = √(γ · R · T/M), where γ is the adiabatic index, R is the universal gas constant, T is the temperature in kelvins, and M is the molar mass of air. Since the frequency of a pipe organ (closed at one end) is directly proportional to the speed of sound and inversely proportional to the length of the pipe, an increase in temperature will lead to a proportional increase in frequency. However, the length of the pipe is constant in this scenario.

Assuming the organ pipe's length is fixed and it produces a fundamental frequency of 384 Hz at 20°C, we can use the formula for the fundamental frequency of a pipe closed at one end, which is f = v/4L. If the temperature increases to 25°C, the speed of sound also increases, leading to an increase in frequency. Therefore, the new frequency can be calculated by considering the proportional change in the speed of sound with temperature.

Answer 2

If the room temperature increases to
`\(22^\circ \mathrm{C}\)`, the frequency of the pipe organ will increase from
`\(384 \mathrm{~Hz}\).`

When room temperature rises, the speed of sound in air increases. As a pipe organ's frequency depends on the speed of sound, a temperature rise from
`\(20^\circ \mathrm{C}\) to \(22^\circ \mathrm{C}\)` will heighten the speed of sound and subsequently raise the organ's frequency.

The change aligns with the direct relationship between temperature and sound speed, resulting in an elevated pitch, causing the frequency to increase from the initial
`\(384 \mathrm{~Hz}\)` measurement at
`\(20^\circ \mathrm{C}\)`.

Question: