Answer to Question #122353 in Physics for Lilly

Question

A source vibration for a sound wave makes 9.8  106

oscillations (cycles) in 3.5 minutes.
If the speed of the sound wave generated is 318.9 m/s, then determine the distance between
2 successive compressions of the sound wave train.

Answer 1

The frequency of the source is the number of oscillations in one second:

$$f = \dfrac{9.8\cdot 10^6}{3.5\cdot 60s} \approx 46.7 kHz$$

The distance between 2 successive compressions of the sound wave is called the wavelength. The wavelength $\lambda$, frequency $f$ and speed $v$ are connected in the following way:

$$\lambda = v/f$$

Substituting the numerical values, get:

$$\lambda = \dfrac{318.9m/s}{46.7\cdot 10^3 Hz} \approx6.81mm$$

Answer. 6.81 mm.