The fundamental frequency of a pipe that is open at both ends is 524 Hz. the frequency of the new fundamental.

Verified step by step guidance

1. Understand that a pipe open at both ends supports standing waves with nodes at both ends. The fundamental frequency is the lowest frequency at which the pipe resonates.
2. The fundamental frequency for a pipe open at both ends is given by the formula: $f=\frac{v}{2L}$, where $v$ is the speed of sound in air and $L$ is the length of the pipe.
3. Given the fundamental frequency is 524 Hz, if the length of the pipe changes, the new fundamental frequency can be calculated using the same formula, adjusting for the new length.
4. If the length of the pipe is halved, the new fundamental frequency will be doubled, because the frequency is inversely proportional to the length of the pipe.
5. Calculate the new fundamental frequency using the formula: $f=\frac{v}{2L}$, substituting the new length of the pipe.

Key Concepts

Fundamental Frequency

The fundamental frequency is the lowest frequency at which a system oscillates. In the context of a pipe open at both ends, it is determined by the speed of sound in air and the length of the pipe. The fundamental frequency is the first harmonic, and it sets the base for other harmonics or overtones.

Open Pipe Harmonics

An open pipe supports standing waves with nodes at both ends. The fundamental frequency corresponds to the first harmonic, where the length of the pipe is half the wavelength of the sound wave. Higher harmonics are integer multiples of the fundamental frequency, allowing the pipe to produce a series of overtones.

Speed of Sound

The speed of sound in air is a crucial factor in determining the frequency of sound waves in a pipe. It is affected by factors such as temperature and pressure. In calculations involving pipes, the speed of sound is used to relate the wavelength of the sound wave to its frequency, using the formula v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength.