# Oscillations and Waves

Computer Science I · Physics · https://tryals.app/learn/computer-science-i/oscillations-and-waves

## Oscillations and SHM

Many systems **oscillate**, repeating a motion around equilibrium. The ideal model is **simple harmonic motion (SHM)**, which occurs when the restoring force is proportional to displacement.

For a mass on a spring, this is described by **Hooke's law**: $F = -kx$. SHM traces a sinusoid defined by:

| Quantity | Symbol & Definition |
| --- | --- |
| **Amplitude** | $A$, maximum displacement |
| **Period** | $T$, time for one full cycle |
| **Frequency** | $f = \frac{1}{T}$, cycles per second in **hertz** |

**Key rule:** The period of SHM does _not_ depend on amplitude. A big swing and small swing take the same time, making pendulums reliable clocks.

> **Pitfall:** Confusing **frequency** and **period**. They are **reciprocals** ($f = 1/T$). High frequency means a _short_ period.

## Waves and Interference

A **wave** is a traveling disturbance carrying **energy** without transporting **matter**. Key wave quantities are **wavelength** $\lambda$ (distance between repeats), frequency $f$, and **speed** $v$, tied by:

$$v = f\lambda$$

Waves are classified by their direction of oscillation relative to travel:

| Wave Type | Oscillation Direction | Example |
| --- | --- | --- |
| **Transverse** | Perpendicular to travel | Light, string |
| **Longitudinal** | Parallel to travel | Sound |

When overlapping waves meet, they **interfere**: **constructive** (reinforcing) or **destructive** (cancelling).

> **Pitfall:** Thinking a wave carries **matter** along with it. A cork bobs in place; the water itself stays put while energy moves.

## Practice questions

5 of this lesson's 10 practice questions, with answers. The full set is in the app.

### 1. Noise-cancelling headphones generate sound to make things quieter. Which principle are they exploiting, and what limits them?

A. Masking, where the added sound makes the noise less noticeable
B. Nothing physical, the effect is psychological
C. Destructive interference, whose limit is timing
D. Sound absorption by the added waveform, which converts it to heat

**Answer:** C. Destructive interference, whose limit is timing

**Why:** The wave is inverted and summed, which is superposition doing arithmetic, and it demands accurate phase, so a predictable 100 Hz hum is easy and a transient is over before the system can respond. The energy is redistributed rather than destroyed, exactly as the interference lesson requires.

Page: https://tryals.app/practice/computer-science-i/oscillations-and-waves/noise-cancelling-headphones-generate-sound-to-make-things-quieter

### 2. Complete the defining property of simple harmonic motion that makes pendulums good clocks.

**Answer:** For an ideal oscillator the period **does not depend on the amplitude**.

**Why:** A large swing covers more distance but moves faster, and the two effects cancel exactly, so the timing is unchanged. That amplitude independence is precisely what allows a pendulum to keep time as friction gradually reduces its swing.

Page: https://tryals.app/practice/computer-science-i/oscillations-and-waves/complete-the-defining-property-of-simple-harmonic-motion-that-makes

### 3. Select every statement that is TRUE of simple harmonic motion and waves.

A. The pull back toward equilibrium grows in proportion to how far you have gone
B. Two overlapping waves add, giving reinforcement or cancellation
C. Dividing a wave's frequency by its wavelength gives its speed
D. A wave transports energy without transporting matter
E. Frequency is the reciprocal of the period

**Answer:** A. The pull back toward equilibrium grows in proportion to how far you have gone; B. Two overlapping waves add, giving reinforcement or cancellation; D. A wave transports energy without transporting matter; E. Frequency is the reciprocal of the period

**Why:** Speed is frequency times wavelength, not divided by it, dividing hertz by metres cannot give metres per second, which is the quickest way to catch the slip. The other four are exactly as taught.

Page: https://tryals.app/practice/computer-science-i/oscillations-and-waves/select-every-statement-that-is-true-of-simple-harmonic-motion-and

### 4. Two identical waves overlap. Sort each described situation by the kind of interference it produces.

**Answer:**

- Constructive: Crest meets crest, Trough meets trough, Two speakers in step reinforce the sound at a point
- Destructive: Crest meets trough, A noise-cancelling headphone adds an inverted copy of the incoming sound

**Why:** Like displacements reinforce and opposite ones cancel, so trough meeting trough is constructive even though the result points downward. Inverting a signal and adding it is destructive interference by design, the whole principle of active noise cancellation.

Page: https://tryals.app/practice/computer-science-i/oscillations-and-waves/two-identical-waves-overlap-sort-each-described-situation-by-the

### 5. Two identical waves meeting exactly out of phase cancel, which means their energy has been destroyed.

**Answer:** False

**Why:** False. Energy is conserved: destructive interference at one point is always accompanied by constructive interference elsewhere, and the total over the whole pattern is unchanged. That is why an interference pattern has bright fringes exactly where the dark ones are missing their energy.

Page: https://tryals.app/practice/computer-science-i/oscillations-and-waves/two-identical-waves-meeting-exactly-out-of-phase-cancel-which-means