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Sound Waves revision notes

Every idea in the Sound Waves chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 18 and download the PDF.

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Sound as a longitudinal wave

Displacement and pressure waves
Δp=−B ∂s∂x,P0=Bks0=ρv ωs0\Delta p=-B\,\frac{\partial s}{\partial x},\qquad P_0=B k s_0=\rho v\,\omega s_0
ss = particle displacement along the wave, BB = bulk modulus, v=B/ρv=\sqrt{B/\rho}. Δp\Delta p is 90∘90^\circ out of phase with ss.
xxcompression: s=0s=0, Δp\Delta p largestssΔp\Delta p
Δp=−B ∂s/∂x\Delta p=-B\,\partial s/\partial x: pressure peaks where displacement is zero
  • Compressions and rarefactions (largest ∣Δp∣|\Delta p|) sit where the displacement is zero; where the displacement is largest, the excess pressure is zero.
  • Quick method. Reading a wave equation: amplitude = half the total to-and-fro distance, ω=2πf\omega=2\pi f, k=2πf/vk=2\pi f/v. In cos⁡2π(at−bx)\cos2\pi(at-bx), f=af=a and λ=1/b\lambda=1/b.
Pressure and displacement nodes
  • Closed end: displacement node, pressure antinode. Open end: displacement antinode, pressure node (pressure stays atmospheric).
  • Reflection at a closed end: the displacement wave comes back inverted, the pressure wave upright. At an open end it is the other way round.
Audible range and echo
t=2dv,dmin⁡=v (0.1 s)2≈17 mt=\frac{2d}{v},\qquad d_{\min}=\frac{v\,(0.1\ \text{s})}{2}\approx17\ \text{m}
Ear holds a sound about 0.1 s. Audible range 20 Hz to 20 kHz; below is infrasound, above is ultrasound.

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15 more concepts in 5 topics

Speed of sound, Intensity and loudness, Organ pipes and resonance tube, Beats and Doppler effect (off syllabus from 2024). Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Speed of sound

  • Newton's formula
  • Laplace correction3×
  • Temperature, pressure, humidity
  • Solids and liquids1×

Intensity and loudness

  • Intensity of a sound wave
  • Point source: inverse square1×
  • Sound level in decibels
  • Pitch, loudness and quality

Organ pipes and resonance tube

  • Open pipe1×
  • Closed pipe2×
  • End correction1×
  • Resonance tube4×

Beats

  • Beat frequency7×
  • Finding an unknown frequency2×

Doppler effect (off syllabus from 2024)

  • Doppler effect in sound18×

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