Solve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?

Inverse variation describes a relationship where one variable increases as the other decreases. In mathematical terms, if two variables x and y vary inversely, their product is constant (xy = k). This concept is crucial for solving problems where one quantity affects another in an opposite manner, such as the relationship between pitch and wavelength in this question.

Wavelength and frequency are fundamental concepts in wave physics, particularly in sound. Wavelength is the distance between successive crests of a wave, while frequency refers to the number of vibrations or cycles per second, measured in hertz (Hz). Understanding how these two quantities relate is essential for solving problems involving sound waves, as they are inversely related in this context.

Setting up proportions is a method used to solve problems involving ratios and relationships between quantities. In this case, knowing the initial pitch and wavelength allows us to create a proportion to find the unknown pitch for a different wavelength. This technique is vital for applying the concept of inverse variation to find the solution effectively.