Example 16.1 (Section 16.1) showed that for sound waves in air with frequency 1000 Hz, a displacement amplitude of 1.2 * 10-8 m produces a pressure amplitude of 3.0 * 10-2 Pa. (a) What is the wavelength of these waves?

Verified step by step guidance

1. Identify the given values: frequency (f) = 1000 Hz, displacement amplitude = 1.2 * 10^-8 m, and pressure amplitude = 3.0 * 10^-2 Pa.
2. Recall the relationship between the speed of sound (v), frequency (f), and wavelength (\(\lambda\)) given by the equation \(v = f \times \lambda\).
3. Determine the speed of sound in air. For typical conditions at room temperature, the speed of sound in air is approximately 343 m/s.
4. Substitute the known values of the speed of sound and frequency into the equation to solve for the wavelength: \(\lambda = \frac{v}{f}\).
5. Calculate the wavelength using the values from the previous steps.

Key Concepts

Wave Properties

Waves are disturbances that transfer energy through a medium without the permanent displacement of the medium itself. Key properties of waves include wavelength, frequency, and amplitude. The wavelength is the distance between successive crests or troughs, while frequency is the number of cycles that pass a point per unit time. Understanding these properties is essential for analyzing wave behavior.

Relationship Between Wave Speed, Frequency, and Wavelength

The speed of a wave is related to its frequency and wavelength by the equation v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. This relationship allows us to calculate one of these properties if the other two are known. For sound waves in air, the speed is approximately 343 m/s at room temperature, which can be used to find the wavelength when the frequency is given.

Pressure Amplitude and Displacement Amplitude

In sound waves, the pressure amplitude is the maximum change in pressure from the ambient atmospheric pressure, while the displacement amplitude refers to the maximum displacement of particles in the medium from their equilibrium position. These amplitudes are related, as greater displacement leads to greater pressure variations. Understanding this relationship is crucial for analyzing how sound waves propagate through different media.