## 18.1.2 Interference of Sound Waves Sound waves, being longitudinal waves, can exhibit interference in a manner similar to transverse waves such as water waves. When sound waves from two **coherent sources** (for example, two speakers connected to the same signal generator) overlap, they create an interference pattern. This pattern consists of regions where the sound is louder and regions where it is quieter. This can be visualized with two speakers facing a screen. A microphone moved across the screen can detect variations in sound intensity. ### Constructive Interference Occurs when the compressions of one wave align with the compressions of another, or rarefactions align with rarefactions. The amplitudes add up, resulting in a louder sound. In Figure 18.4, this happens at points such as $\mathrm{P}_1$, $\mathrm{P}_4$, $\mathrm{P}_5$, $\mathrm{P}_6$ and $\mathrm{P}_9$. For constructive interference, the path difference ($\Delta L$) must be an integer multiple of the wavelength: $$\Delta L = n\lambda \quad \text{where } n = 0, 1, 2, \dots$$ ### Destructive Interference Occurs when the compression of one wave aligns with the rarefaction of another. The amplitudes cancel each other out, resulting in a quieter sound. In Figure 18.4, this happens at points such as $\mathrm{P}_2$, $\mathrm{P}_3$, $\mathrm{P}_7$ and $\mathrm{P}_8$. For destructive interference, the path difference ($\Delta L$) must be an odd half-integer multiple of the wavelength: $$\Delta L = (n + \frac{1}{2})\lambda \quad \text{where } n = 0, 1, 2, \dots$$ A practical application of this principle is found in **noise-cancelling headphones**, which generate sound waves to destructively interfere with ambient noise. ### Coherent Sources Sources that emit waves of the same frequency and with a constant phase difference. For sound, this can be achieved by connecting two speakers to the same signal generator. ### Constructive vs. Destructive Interference | Type of Interference | Wave Alignment | Resulting Sound | | :--- | :--- | :--- | | **Constructive** | Compression + Compression
Rarefaction + Rarefaction | Louder (Increased Amplitude) | | **Destructive** | Compression + Rarefaction | Quieter (Decreased Amplitude) |