For the wave in Fig. 15.2, what is the frequency of the second harmonic if the distance between two pressure nodes is 30 cm? The speed of sound in air is 343 m/s.
A)f = 190.6 Hz
B)f = 381.1 Hz
C)f = 571.7 Hz
D)f = 1143.3 Hz

Question

Quizplus · Accepted Answer

The frequency of the second harmonic (n=2) in a wave can be calculated using the formula $f_n = \frac{n \cdot v}{2L}$, where $v$ is the speed of sound, $L$ is the length of the wave, and $n$ is the harmonic number. For the second harmonic, $n=2$, and given that the distance between two pressure nodes (half the wavelength, $\lambda/2$) is 30 cm (0.3 m), the full wavelength ($\lambda$) is 0.6 m. Thus, $L = \lambda/2 = 0.3 m$. Plugging the values into the formula gives $f_2 = \frac{2 \cdot 343 m/s}{2 \cdot 0.3 m} = 381.1 Hz$.

For the Wave in Fig