Beats: tuning one string against another
"Beats: tuning one string against another" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Beats" in Waves. Heard together, the two notes swell and fade. The shaded band is how loud the sound is from moment to moment; the fast wiggle inside it, near 427 Hz, is too quick to draw. Two close frequencies give a sound at their average whose loudness rises and falls ν₁ − ν₂ times a second. As the strings come into tune the beats slow down, and they vanish when the frequencies match. JEE Main asked 27 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Beats in Waves. Change the values and watch what happens.
In JEE Main
42 shifts analysed
27 questions from Waves across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §14.7
- Two sounds of nearly equal frequency heard together give a sound at their average frequency whose loudness swells and fades regularly. This waxing and waning is called beats.
- For two waves of equal amplitude, s = s₁ + s₂ = [2a cos ω_b t] cos ω_a t, with ω_b = (ω₁ − ω₂)/2 and ω_a = (ω₁ + ω₂)/2.
- When |ω₁ − ω₂| is small compared with ω₁ + ω₂, the term cos ω_a t is a fast oscillation and 2a cos ω_b t is a slowly changing amplitude around it.
- The loudness peaks whenever cos ω_b t reaches +1 or −1, which happens twice in each period of cos ω_b t. So the beat frequency is ν_beat = ν₁ − ν₂.
- Example: waves of 11 Hz and 9 Hz give a resultant at 10 Hz that swells and fades 2 times a second.
- Musicians use beats to tune instruments: they adjust one against a reference until the beats slow down and vanish.
- Worked example (NCERT): sitar string A plays Dha at 427 Hz, and 5 beats per second are heard with string B, so B is 422 Hz or 432 Hz. Tightening B raises its frequency and the beats drop to 3 per second; only 422 Hz moves towards 427 Hz, so ν_B = 422 Hz.
- Musical pillars: the Nellaiappar temple in Tamil Nadu, built by the Pandyan dynasty in the 7th century, has stone pillars that give musical notes (Sa Re Ga Ma Pa Dha Ni Sa) when tapped, grouped as Shruti, Gana Thoongal and Laya Thoongal pillars. Such pillars are also found at Hampi, Kanyakumari and Thiruvananthapuram.
Questions
3 answers
- What does the "Beats: tuning one string against another" simulation show?
- Heard together, the two notes swell and fade. The shaded band is how loud the sound is from moment to moment; the fast wiggle inside it, near 427 Hz, is too quick to draw.
- Does JEE Main ask questions from Waves?
- Yes. JEE Main asked 27 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Beats" in Waves (Class 11 Physics).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.