The speed of sound in air is 344 m>s at room temperature. The lowest frequency of a large organ pipe is 30 s-1 and the highest frequency of a piccolo is 1.5 * 104 s-1. Determine the difference in wavelength between these two sounds.

Starting with the basics, the speed of sound refers to how fast sound waves travel through a medium. This medium can be a solid, liquid, or gas. The speed at which sound travels can be affected by various factors, including temperature, humidity, and air pressure. In our exercise, we're considering the speed of sound in air at room temperature, which is given as 344 meters per second (m/s).

This value is not arbitrary; it is a determined speed at a given temperature of approximately 20°C. It's crucial to recognize that sound travels faster in warmer air and slower in colder air because the molecules move more vigorously at higher temperatures. Understanding this parameter is fundamental because it aids in solving problems related to sound waves, such as calculating wavelengths and frequencies.

Frequency, in the context of sound waves, refers to the number of vibrations or cycles per second. It is measured in Hertz (Hz), where one Hertz is equivalent to one cycle per second. In our textbook exercise, we analyze two distinct frequencies: a large organ pipe with a low frequency of 30 Hz and a piccolo which produces a much higher frequency of 15,000 Hz (1.5 * 10^4 Hz).

The frequency of a sound wave is directly linked to our perception of pitch; a higher frequency corresponds to a higher pitch and vice versa. This concept is important as it connects with the wavelength and helps determine the pitch of sounds, which is a central theme in music, acoustics, and audio engineering fields. When calculating wavelength differences, understanding the frequency component of sound waves allows us to visualize the physical length between the peaks of each wave for different sounds.

The wavelength of a sound wave is the physical distance from one point of a wave to the identical point on the next wave. Think of it as measuring the distance from one wave's crest to the next crest. It is represented by the Greek letter lambda (\( \text{\lambda} \text{\). In a formulaic relationship, wavelength is inversely related to frequency and can be computed if the speed of sound in the medium is known, using the equation \( \text{\lambda} = \frac{v}{f} \). In simpler terms, as frequency increases, the wavelength of the sound decreases, and as frequency decreases, the wavelength increases.}

Related to the exercise, we observed this inverse relationship when calculating the wavelength for two sounds with differing frequencies. A lower frequency sound, such as from the organ pipe, has a longer wavelength, whereas a high-frequency sound from the piccolo has a shorter wavelength. By computing these wavelengths, we can find out how far apart sound waves are for two drastically different musical instruments. This becomes particularly useful when studying the physics of music and designing instruments and concert halls for optimal acoustics.