GCSE Physics: Longitudinal & Transverse Waves, Labelling & Calculating Wave Speed

Summary

This video from Cognito provides a comprehensive overview of waves for GCSE Physics. It explains the fundamental function of waves in transferring energy, not matter. The video details how to accurately label the parts of a wave using displacement-distance graphs, including amplitude, wavelength, crest, and trough. It then moves on to calculating wave frequency using displacement-time graphs and the time period, introducing the formula $f = 1/T$. Finally, the video explains how to calculate wave speed using the equation $v = f\lambda$ and distinguishes between transverse and longitudinal waves with clear examples of each.

Key Takeaways

* **Waves transfer energy, not matter.** This is the fundamental role of any wave.

* **Displacement-Distance Graphs** are used to visualize a wave at a single point in time. Key labels include:

* **Amplitude:** The maximum displacement from the equilibrium position.

* **Wavelength ($\lambda$):** The distance between two consecutive identical points on a wave (e.g., crest to crest or trough to trough).

* **Crest:** The highest point of a wave.

* **Trough:** The lowest point of a wave.

* **Displacement-Time Graphs** are used to visualize the displacement of a point on a wave over time. Key labels include:

* **Time Period (T):** The time taken for one complete wave to pass a point.

* **Frequency (f)** is the number of waves passing a point per second and is calculated using the formula: $f = 1/T$. Frequency is measured in Hertz (Hz).

* **Wave Speed (v)** is the speed at which a wave travels and is calculated using the formula: $v = f\lambda$.

* **Transverse Waves:** The oscillations are perpendicular to the direction of energy transfer. Examples include light waves and waves on a string.

* **Longitudinal Waves:** The oscillations are parallel to the direction of energy transfer. Examples include sound waves and P-waves (seismic waves).

Detailed Notes

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1. The Function of Waves (0:00 Introduction to Waves)

* **Core Function:** Waves are a mechanism for transferring **energy**.

* **Crucial Distinction:** Waves **do not** transfer matter. Particles oscillate but return to their original positions.

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2. Labelling a Wave (Displacement-Distance Graph) (1:03)

* **Visualisation:** A displacement-distance graph shows the shape of a wave at a specific moment in time.

* **Key Components to Label:**

* **Equilibrium Position:** The undisturbed position of the medium.

* **Displacement:** The distance of a point on the wave from the equilibrium position.

* **Amplitude (A):** The maximum displacement from the equilibrium position. Measured in meters (m).

* **Crest:** The highest point of the wave.

* **Trough:** The lowest point of the wave.

* **Wavelength ($\lambda$):** The horizontal distance between two consecutive identical points on the wave. This can be measured from crest to crest, trough to trough, or between any two corresponding points. Measured in meters (m).

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3. Calculating Wave Frequency (Displacement-Time Graph & Time Period) (2:02 - 2:28)

* **Visualisation:** A displacement-time graph shows how the displacement of a single point on a wave changes over time.

* **Time Period (T):** The time it takes for one complete wave to pass a fixed point. Measured in seconds (s).

* **Frequency (f):** The number of complete waves that pass a fixed point every second. Measured in Hertz (Hz).

* **Relationship:** Frequency and time period are inversely proportional.

* Formula: **$f = 1 / T$**

* If the time period is short, the frequency is high, and vice-versa.

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4. Calculating Wave Speed (3:42 - 4:42)

* **The Wave Speed Equation:** This equation links the speed, frequency, and wavelength of a wave.

* Formula: **$v = f \lambda$**

* Where:

* $v$ = wave speed (meters per second, m/s)

* $f$ = frequency (Hertz, Hz)

* $\lambda$ = wavelength (meters, m)

* **Worked Example (4:05):**

* A wave has a frequency of 5 Hz and a wavelength of 0.2 m.

* Calculate its speed:

* $v = f \lambda$

* $v = 5 \text{ Hz} \times 0.2 \text{ m}$

* $v = 1 \text{ m/s}$

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5. Transverse vs. Longitudinal Waves (4:42)

* **Key Difference:** The direction of oscillation of the particles in the medium relative to the direction of energy transfer.

* **Transverse Waves:**

* **Oscillations are perpendicular** to the direction of energy transfer.

* Imagine shaking a rope up and down – the wave moves horizontally along the rope, but the rope segments move vertically.

* **Examples:**

* Light waves (electromagnetic waves)

* Waves on a string or rope

* Water waves (though they have a component of longitudinal motion too)

* **Features:** Have crests and troughs.

* **Longitudinal Waves:**

* **Oscillations are parallel** to the direction of energy transfer.

* Imagine pushing and pulling a Slinky – the compressions and rarefactions move along the Slinky, and the coils also move back and forth along the Slinky.

* **Examples:**

* Sound waves

* P-waves (primary seismic waves)

* Ultrasound waves

* **Features:** Consist of compressions (areas of high pressure/density) and rarefactions (areas of low pressure/density).