MHT-CET Physics · Sound

Sound Waves: Speed, Energy and Loudness

Sound is a mechanical wave that needs a medium, travels at v = fλ, carries energy proportional to the square of its amplitude times the square of its frequency, and is measured in decibels, where every 10 dB is ten times the intensity.

All Sound notes MHT-CET Physics strategy

Why this matters

6 PYQs, one HARD: the distance a sound travels in a number of vibrations, how many times more intense one decibel level is than another, the amplitude that keeps energy equal at a lower frequency, the speed of sound in a gas mixture, and which statements and instruments fit. One card.

Concept 1 of 1: Speed, Energy and Decibels

Each vibration sends the wave one wavelength further, so n vibrations cover nλ = nv/f. A wave's energy goes as A²f², so at a third of the frequency the amplitude must be three times larger to carry the same energy. Loudness in decibels is 10 log(I/I₀): a 30 dB difference is 10³ = 1000 times the intensity. Sound cannot cross a vacuum. In a gas its speed is √(γRT/M); for a mixture, average the molar mass and the specific heats by moles first.

Definition

$v = f\lambda$ ; n vibrations cover $n\lambda$ (480 Hz at 320 m/s, 180 vibrations ⇒ 120 m).
Energy $\propto A^2 f^2$ : equal energy at f/3 ⇒ 3A.
$L = 10\log\dfrac{I}{I_0}$ dB: ΔL of 10n dB ⇒ $10^n$ times the intensity.
$v = \sqrt{\dfrac{\gamma RT}{M}}$ ; mixture: mole-weighted M and $C_v$ (1 mol He + 2 mol O₂ at 27 °C ⇒ 401 m/s).
Sound needs a medium; percussion instruments are struck (a clarinet is blown).

Wave speed and loudness

v = f\lambda, \qquad L = 10\log_{10}\frac{I}{I_0}

Worked example

A 500 Hz sound travels at 340 m/s. Its wavelength, and the distance covered in 100 vibrations?

Practice this conceptself-check · 1 quick reps

The same idea in a real exam question:

MHT-CET · 2023 · 10th May Shift 1 · Q48Moderate

Example 1 · Sound · Sound Wave Properties, Speed, and Intensity

A musical instrument X produces sound waves of frequency

n

and amplitude

A

. Another musical instrument Y produces sound waves of frequency

\frac{n}{3}

. The waves produced by X and Y have equal energies. The amplitude of waves produced by Y will be

Treating decibels as linear

60 dB is not twice as intense as 30 dB. Each 10 dB multiplies the intensity by 10, so 30 dB more is 1000 times.

Holding amplitude fixed when frequency changes

Energy goes as A²f². To keep it equal at a third of the frequency, the amplitude must triple.

Drill 5 more on speed, energy and decibels

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Speed, Energy and Decibels
Wave speed and loudness
$v = f\lambda, \qquad L = 10\log_{10}\frac{I}{I_0}$

Watch out for (2)

Treating decibels as linear
→ Speed, Energy and Decibels
Holding amplitude fixed when frequency changes
→ Speed, Energy and Decibels

Test yourself on Sound

15 past MHT-CET questions from this chapter, timed at 14 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Sound chapter test Drill all 6 questions