When the source and the wave move at the same velocity | Physics | Khan Academy

TL;DR

When the velocity of the source is equal to the velocity of the wave, the observed period becomes zero and the frequency becomes undefined, approaching infinity.

Transcript

In the last several videos, we assumed that the velocity of the source, of the object that's emitting the wave, we've assumed that that's less than the velocity of the wave. And we saw what happens with the Doppler effect and all of that. But what I want to do in this video is not make this assumption. In particular, let's see what happens, at leas... Read More

Key Insights

• 👋 When the velocity of the source is equal to the velocity of the wave, the observed period becomes zero and the frequency becomes undefined.
• 🤲 The waveform gets infinitely bunched together, resembling one impulse.
• 👂 All of the sound energy reaches the observer at the same time, resulting in a thumping sound.
• 💥 This phenomenon is similar to a sonic boom experienced in supersonic speeds.
• 0️⃣ The frequency formula becomes undefined because the divisor approaches zero.
• 👋 The assumption that the source velocity is less than the wave velocity is no longer valid in this scenario.
• 👋 The understanding of these concepts is not limited to soundwaves but can be applied to any type of wave.

Questions & Answers

Q: What happens to the observed period when the velocity of the source is equal to the velocity of the wave?

When the velocities are equal, the observed period becomes zero, meaning there is no waiting time between successive crests. The entire waveform becomes infinitely bunched together.

Q: What is the effect on frequency when the velocity of the source equals the velocity of the wave?

The frequency becomes undefined at the speed of the wave, but it approaches infinity as the source approaches the velocity of the wave. This is because the divisor in the frequency formula becomes a very small positive number.

Q: What does it mean when the frequency is undefined?

When the frequency is undefined, it means that all of the sound energy reaches the observer at the same time, resulting in a thumping sound instead of a periodic pitch. This is commonly experienced in trans-sonic or supersonic speeds, similar to a sonic boom.

Q: How does the wave reach the observer when the velocity of the source equals the velocity of the wave?

When the wave reaches the observer, all of the wave fronts smack the observer at once. Instead of hearing something periodic, the observer hears a big thump because all of the energy is arriving simultaneously.

Summary & Key Takeaways

• In previous videos, the assumption was made that the velocity of the source is less than the velocity of the wave.

• When the velocity of the source is equal to the velocity of the wave, the observed period becomes zero and the entire waveform gets bunched together.

• The frequency becomes undefined at the speed of the wave, but it approaches infinity as the source approaches the velocity of the wave.