Waves

Types of waves:

• Transverse: oscillations perpendicular to wave direction (light, EM waves, water waves)
• Longitudinal: oscillations parallel to wave direction (sound, ultrasound)

Key terms:

• Amplitude (A): maximum displacement from equilibrium (height of wave)
• Wavelength (λ): distance between two identical points on adjacent waves
• Frequency (f): waves passing a point per second (Hz)
• Period (T): time for one complete wave (T = 1/f)

Wave equation: v = fλ (wave speed = frequency × wavelength)

Sound: longitudinal wave, needs a medium (can't travel in vacuum). Speed in air ~340 m/s.

The electromagnetic spectrum (increasing frequency / decreasing wavelength): Radio → Microwaves → Infrared → Visible light → UV → X-rays → Gamma rays

All travel at 3 × 10⁸ m/s in a vacuum.

Reflection: angle of incidence = angle of reflection (measured from normal). Refraction: waves bend when speed changes (entering glass, light slows → bends towards normal).

Deep dive: build the idea, then use it

Conceptual model

A wave transfers energy and information without carrying material from source to destination overall. In transverse waves, vibrations are perpendicular to travel; in longitudinal waves they are parallel, producing compressions and rarefactions. Frequency counts oscillations each second, wavelength is one complete repeat, and v=fλ ties them together. At a boundary, speed may change, causing refraction.

Worked example

A wave has frequency 50 Hz and wavelength 0.68 m. v=fλ=50×0.68=34 m s⁻¹. If frequency stays fixed as it enters another medium and speed decreases, λ=v/f means wavelength decreases too. This is why a ray can bend: one part of the wavefront changes speed before the other.

Exam-method habit

Read one whole wavelength between matching points, such as crest to crest. Convert units before using v=fλ, and include units in every line. In a wave sketch, label amplitude separately from wavelength. For a ray diagram, draw the normal first and measure angles from it, not from the surface.

Common errors to catch early

Calling amplitude the distance from crest to trough; mixing hertz with seconds; assuming sound travels through a vacuum; saying refraction happens because light “likes” to bend; and reversing frequency and wavelength when speed is fixed.

Retrieval drill — close the notes, phir try karo

Classify sound, light, and a stretched-spring pulse. A 200 Hz sound has wavelength 1.7 m: find speed. What changes when amplitude increases? Explain why a reflected ray has equal angles to the normal.

A Pakistan-relevant use

An auditorium team can reduce echo by combining absorbent surfaces with sensible speaker placement. Sound-wave reflection explains the issue; testing the space with people present is still important because furnishings and audience size change the result.

Concise summary

Describe the vibration, connect speed-frequency-wavelength, and use a normal for ray geometry. Waves move energy through a medium—or, for electromagnetic waves, through vacuum—by a clear physical pattern.

A reliable self-check routine

Before accepting an answer, say what each quantity, symbol, particle, or graph feature means. Then check its unit, sign, direction, size, or conservation rule. In a calculation, write the relationship first, substitute with units, calculate, and decide whether the result is sensible. In an explanation, make a chain: cause → mechanism → observed result. This is not extra decoration; it is how a reader can follow your thinking and how you catch a copied digit or an attractive-but-wrong statement. If the question gives a new context, do not hunt for a memorised sentence. Identify the model underneath it and apply that model. Short, precise working beats a long paragraph that never answers the command word.

Practice plan

Try one straightforward question without notes, one mixed question where you choose the method, and one question where you explain why an answer is reasonable. Mark the exact first step that felt uncertain. Revisit that step the next day for two minutes instead of rereading everything. Small retrieval loops make the topic stick, yaar.

Connect and transfer

This topic becomes stronger when you deliberately meet it in an unfamiliar wrapper. A diagram may be rotated, a calculation may use an awkward unit, a practical may describe an everyday object, or a question may provide more information than you need. Pause and sort the information into three columns: given, wanted, and relationship. That small pause prevents the common rush of putting every number into the first formula remembered. If the answer is qualitative, decide whether the task is asking for a prediction, a description, or a mechanism; these need different sentences. If it is numerical, estimate its order of magnitude before the calculator. If it involves a graph or table, describe the relevant trend using the actual variables before explaining it.

Teach the idea out loud in sixty seconds as though a friend missed the lesson. Avoid specialist words you cannot unpack. Then add those words back with their exact meaning. This exposes the difference between recognition (“that looks familiar”) and recall (“I can construct the answer”). Keep an error log with a corrected example, not a list of scores. For the next attempt, cover the correction and reproduce the decision that led to it. The goal is calm, repeatable reasoning—not racing through a page. When your final answer differs from a friend’s, compare the model and assumptions before comparing calculators. Often the useful learning is in the first different step.