Understanding the Impact of Phase Differences in Sinusoids

What is the result when two sinusoids at 150 Hz with a peak amplitude of 2 are 180 degrees out of phase?

• A. 150 Hz sinusoid with a peak amplitude of 0.0
• B. 150 Hz sinusoid with a peak amplitude of 4.0
• C. 300 Hz sinusoid with a peak amplitude of 0.0
• D. 300 Hz sinusoid with a peak amplitude of 4.0

Answer: (A)

When two sinusoids are out of phase by 180 degrees, they effectively cancel each other out. In this scenario, both sinusoids have the same frequency of 150 Hz and a peak amplitude of 2. The 180-degree phase difference indicates that when one sinusoid reaches its positive peak, the other is at its negative peak of equal amplitude. As a result, when the two sinusoids combine, their contributions to the overall signal negate one another. Mathematically, this cancellation results in a composite signal with an amplitude of 0. Therefore, the outcome is a sinusoid at 150 Hz but with a peak amplitude of 0.0. This aligns with the concept that the superposition of two equal but opposite amplitudes leads to a net amplitude of zero. This analysis clarifies why the selected answer is indeed the correct interpretation of the situation.

When dealing with waveforms, especially in the realms of sound and acoustics, understanding phase difference is crucial. It’s fascinating how something as simple as two sinusoids — or waves — with a peak amplitude can create a greater understanding of sound dynamics. So, let’s break this down a bit.

Imagine you have two sinusoids at 150 Hz, both rocking out with a peak amplitude of 2. The catch? They’re 180 degrees out of phase. Sounds complicated, right? But here’s the kicker: when they’re out of phase like this, they essentially "cancel" each other out. Yup, they negate one another's signals. So, what’s left? A sinusoid at 150 Hz, but with a peak amplitude of… drumroll, please… 0.0!

How does that work? When one sinusoidal wave reaches its positive peak, the other hits its negative peak. Think of it visually: one wave shooting up while the other crashes down, and when you combine these two, you just end up with a flat line. Imagine two friends trying to lift something heavy together but pulling in opposite directions – it just doesn’t lift!

In mathematical terms, this cancellation effect can be described as superposition. The principle of superposition tells us that if two or more waves interact, the resulting wave is the sum of these individual waves. However, in this scenario, where they are equal but opposite, what you end up with is a net amplitude of zero. This might sound a bit theoretical, but it connects directly to practical aspects of sound design and audio engineering, where phase relationships can either enhance or disrupt sound quality.

This exploration of phase differences is particularly relevant for students preparing for the Praxis SLP Licensure Exam. Understanding these principles equips future speech-language pathologists with a stronger foundation in acoustics and sound dynamics. These concepts are not just abstract ideas; they are fundamental to understanding how we process sounds and speech.

So, while waveforms and sinusoidal relationships might seem like niche topics, they’re applicable to everyday situations. Next time you're listening to music, think about how those sound waves interact. Are they working together in harmony or clashing? It’s pretty incredible how waves, through their peaks and troughs, can illustrate the complexities of our auditory world.

To sum it up: when two sinusoids at 150 Hz are 180 degrees out of phase, you get a composite signal that amounts to nothing—the peak amplitude is 0.0. This insight lays the groundwork for understanding more complex interactions in sound and signals. Now, isn’t that a wave of knowledge worth riding?