understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency (understanding of the Doppler effect for a stationary source and a moving observer is not required)

Doppler Effect for Sound Waves

Objective: Understand how the motion of a sound source relative to a stationary observer changes the frequency we hear.

What is the Doppler Effect?

When a sound source moves, the waves it creates are compressed in front of it and stretched behind it. This changes the wavelength and therefore the frequency you hear. 🎧🚗

Key Formula

ScenarioFormula
Source moving towards observer\$f' = f \frac{v}{v - v_s}\$
Source moving away from observer\$f' = f \frac{v}{v + v_s}\$

Analogy: The Running Runner

Picture a runner (the source) shouting a whistle while sprinting towards you. The sound waves in front of the runner are squeezed together, so you hear a higher pitch. When the runner turns and moves away, the waves stretch out, giving a lower pitch. This is exactly what happens with any moving source of sound.

Step‑by‑Step Example

  1. Speed of sound in air: \$v = 340\,\text{m/s}\$.

  2. Source emits a tone of \$f = 500\,\text{Hz}\$.

  3. Source speed: \$v_s = 20\,\text{m/s}\$ towards you.

  4. Calculate observed frequency: \$f' = 500 \times \frac{340}{340-20} \approx 500 \times \frac{340}{320} \approx 531\,\text{Hz}\$.

  5. Result: You hear a slightly higher pitch (≈ 531 Hz).

What If the Source Moves Away?

Use the second formula: \$f' = 500 \times \frac{340}{340+20} \approx 500 \times \frac{340}{360} \approx 472\,\text{Hz}\$. The pitch drops.

Exam Tips

🔍 Remember: The sign in the denominator changes with direction: minus for approaching, plus for receding.

🧮 Quick check: If \$v_s\$ is small compared to \$v\$, the change in frequency is small.

📚 Practice: Work through problems with different \$v_s\$ values to see the trend.

Common Mistakes

  • Using the wrong sign in the formula.

  • Confusing \$v\$ (speed of sound) with \$v_s\$ (speed of source).

  • Assuming the observer is moving when they are actually stationary.

Quick Quiz

1️⃣ If a source moves at \$30\,\text{m/s}\$ towards you and emits \$400\,\text{Hz}\$, what frequency do you hear? (Use \$v = 340\,\text{m/s}\$.)

2️⃣ What happens to the observed frequency if the source moves faster?

💡 Answer 1: \$f' = 400 \times \frac{340}{340-30} \approx 400 \times \frac{340}{310} \approx 439\,\text{Hz}\$.

💡 Answer 2: The observed frequency increases when approaching, decreases when receding.

Takeaway

When a sound source moves relative to a stationary observer, the waves get compressed or stretched, changing the frequency you hear. The key formula and the sign convention are all you need to solve exam questions on this topic.