#beat frequency

Doppler Effect

Two strings produce beats of 4 Hz. One has a frequency of 320 Hz. When the tension in the second string is increased, th

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. Let v₂ be the original frequency. |320 - v₂| = 4 ⇒ v₂ = 316 Hz or 324 Hz . Increasing tension increases frequency. If v₂ = 316 , new v₂’ > 316 , beat = 320 - v₂’ < 4 , becomes 2 Hz ( v₂’ = 318 ), consistent. If v₂ = 324 , beat increases, contradicts. So, v₂

Ref: NCERT > Physics Book > Waves > Doppler Effect

View Details

Beats Phenomenon

What is the significance of the beat frequency when two sound waves interfere?

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. The beat frequency, |f₁ - f₂| , is the rate at which amplitude modulates, perceived as periodic loudness variations, equal to the difference in wave frequencies. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Difference in frequencies, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

View Details

Beats Phenomenon

Two waves of frequencies 496 Hz and 502 Hz interfere. How many beats are heard in 10 seconds?

**Beat formation** is interference in time with time-varying amplitude. Frequencies close together generate slow modulation, count in given duration obtained by multiplying beat frequency by duration, e.g., 6 Hz × 5 s = 30 beats. Beat frequency: vbₑₐt = 502 - 496 = 6 Hz . Beats in 10 s: 6 × 10 = 60 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 60, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

View Details

Beats Phenomenon

Two strings produce beats of 3 Hz. One has a frequency of 400 Hz. When the tension in the second string is slightly incr

**Superposition of nearly equal frequencies** creates resultant y = 2A cos(Δω·t/2) sin(ω_avg·t), envelope frequency Δf/2, beat frequency Δf. Total beats heard in Δt is f_beat·Δt, explaining counting over seconds. Let v₂ be the original frequency. |400 - v₂| = 3 ⇒ v₂ = 397 Hz or 403 Hz . Increasing tension increases frequency. If v₂ = 397 , new v₂’ > 397 , beat = 400 - v₂’ < 3 , becomes 2 Hz, consistent ( v₂’ = 398 ). If v₂ = 403 , beat increases, contradicts. So, v₂ = 397 Hz . Using v = fλ and standing-wave condition fₙ = n v/(2L)

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

View Details

Beats Phenomenon

Two strings produce beats of 3 Hz. One has a frequency of 288 Hz. When the tension in the second string is increased, th

**Beat formation** is interference in time with time-varying amplitude. Frequencies close together generate slow modulation, count in given duration obtained by multiplying beat frequency by duration, e.g., 6 Hz × 5 s = 30 beats. Let v₂ be the original frequency. |288 - v₂| = 3 ⇒ v₂ = 285 Hz or 291 Hz . Increasing tension increases frequency. If v₂ = 285 , new v₂’ > 285 , beat = 288 - v₂’ < 3 , becomes 1 Hz ( v₂’ = 287 ), consistent. If v₂ = 291 , beat increases, contradicts. So, v₂ = 285 Hz . Using v = fλ and

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

View Details

Beats Phenomenon

Two waves of frequencies 520 Hz and 526 Hz interfere. How many beats are heard in 10 seconds?

**Beat formation** is interference in time with time-varying amplitude. Frequencies close together generate slow modulation, count in given duration obtained by multiplying beat frequency by duration, e.g., 6 Hz × 5 s = 30 beats. Beat frequency: vbₑₐt = 526 - 520 = 6 Hz . Beats in 10 s: 6 × 10 = 60 . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 60, illustrating frequency-length-speed interdependence and quantization by boundaries.

Ref: NCERT > Physics Book > Waves > Beats Phenomenon

View Details