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MHT-CET Physics · Formula sheet

Sound formulas

5 formulas and 12 common traps for MHT-CET Physics Sound, grouped by subtopic.

Full notes with worked examples

Sound Waves: Speed, Energy and Loudness

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Speed, Energy and Decibels

Wave speed and loudness

v=fλ,L=10log⁡10II0v = f\lambda, \qquad L = 10\log_{10}\frac{I}{I_0}

Common traps

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.

Organ Pipes, Resonance and Beats

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Open and Closed Pipes

Pipe frequencies

fopen=nv2L,fclosed=(2n−1)v4Lf_{\text{open}} = \frac{nv}{2L}, \qquad f_{\text{closed}} = \frac{(2n - 1)v}{4L}

Resonance Tubes, Strings and Beats

Strings and beats

fn=n2lTμ,fbeat=∣f1−f2∣f_n = \frac{n}{2l}\sqrt{\frac{T}{\mu}}, \qquad f_{\text{beat}} = |f_1 - f_2|

Common traps

Numbering overtones as harmonics

The first overtone is the SECOND harmonic of an open pipe but the THIRD of a closed pipe. Convert every overtone to its harmonic before setting frequencies equal.

Allowing even harmonics in a closed pipe

A closed pipe has only odd harmonics: v/4L, 3v/4L, 5v/4L. There is no 2v/4L.

Adding one end correction to an open pipe

An open pipe has two open ends, so its effective length is l + 1.2r (0.6r at each end); a closed pipe adds only 0.6r.

Reporting mass per unit length as the mass

√(T/μ) gives μ in kg/m. A 0.5 m string with μ = 0.02 kg/m has mass 10 g, not 20 g.

Adding frequencies to get beats

Two notes beat at the DIFFERENCE of their frequencies. 256 Hz and 260 Hz give 4 beats a second.

Taking the first resonance for the least water

The least water gives the LONGEST air column that still resonates. In a 1.5 m tube with λ = 1 m, that is 1.25 m of air and 25 cm of water.

The Doppler Effect

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The Doppler Formula

Doppler effect

f′=f v±vov∓vsf' = f\,\frac{v \pm v_o}{v \mp v_s}

Passing Sources, Echoes and Changing Speeds

Echo from a wall

n′=n v+V1v−V1n' = n\,\frac{v + V_1}{v - V_1}

Common traps

Treating moving source and moving observer alike

The observer's speed sits in the numerator, the source's in the denominator. At 50 m/s the moving source gives 330/280; the moving observer only 380/330.

Getting the sign for recession

Moving apart LOWERS the pitch: observer v − v_o on top, source v + v_s underneath.

Using the source formula twice for an echo

The wall receives as a stationary observer and re-sends as a stationary source; the driver is a source on the way out and an OBSERVER on the way back. The two steps use different places in the formula.

Using one Doppler factor for before and after a pass

Approaching, the source term is v − v_s; receding, v + v_s. The before-to-after ratio is (v + v_s)/(v − v_s), not the square of either factor.

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