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Sound Wave formulas

Master Sound Wave through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Sound Wave, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Speed of sound (general)
$v = \frac{E}{ρ}$
Q1MCQSpeed general
The speed of sound in a medium is:
- A
  $\sqrt{\dfrac{E}{\rho}}$
- B
  $\sqrt{\dfrac{\rho}{E}}$
- C
  $E\rho$
- D
  $\dfrac{E}{\rho}$
Speed in a gas (Newton–Laplace)
$v = \frac{γ P}{ρ} = \frac{γ R T}{M}$
Q1MCQSpeed in gas
The speed of sound in a gas is:
- A
  $\sqrt{\dfrac{\gamma P}{\rho}}$
- B
  $\sqrt{\dfrac{P}{\rho}}$
- C
  $\sqrt{\dfrac{\rho}{\gamma P}}$
- D
  $\gamma P\rho$
Speed in a solid
$v = \frac{Y}{ρ}$
Q1MCQSpeed in solid
The speed of sound in a solid rod is:
- A
  $\sqrt{\dfrac{Y}{\rho}}$
- B
  $\sqrt{\dfrac{\rho}{Y}}$
- C
  $Y\rho$
- D
  $\sqrt{\dfrac{\gamma P}{\rho}}$
Wave relation
$v = f λ$
Temperature dependence
$v \propto T$
Q1MCQTemperature
The speed of sound in air varies with absolute temperature as:
- A
  $\sqrt{T}$
- B
  $T$
- C
  $\dfrac{1}{T}$
- D
  $T^{2}$
Intensity
$I = \frac{P}{A} = 2 π^{2} f^{2} A^{2} ρ v$
Q1MCQIntensity
The intensity of a sound wave is proportional to:
- A
  $f^{2}A^{2}$
- B
  $fA$
- C
  $\dfrac{1}{A^{2}}$
- D
  $f$
Intensity level (decibel)
$L = 10 lo g_{10} \frac{I}{I _{0}} dB$
Q1MCQDecibel
The sound intensity level in decibels is:
- A
  $10\log_{10}\dfrac{I}{I_0}$
- B
  $\dfrac{I}{I_0}$
- C
  $\log I$
- D
  $10\dfrac{I}{I_0}$
Displacement wave
$y = A sin (ω t - k x)$
Q1MCQDisplacement wave
A travelling sound wave can be written as:
- A
  $A\sin(\omega t-kx)$
- B
  $A\sin(\omega t)$
- C
  $Ae^{\omega t}$
- D
  $A\omega t$
Pressure amplitude
$Δ P_{0} = B A k = ρ v ω A$
Q1MCQPressure amplitude
The pressure amplitude of a sound wave is:
- A
  $\rho v\omega A$
- B
  $\rho v A$
- C
  $\dfrac{A}{\rho v}$
- D
  $\omega A$
Beats
$f_{b e a t} = ∣ f_{1} - f_{2} ∣$
Closed pipe fundamental
$f = \frac{v}{4 L}$
Q1MCQClosed pipe
The fundamental frequency of a closed organ pipe is:
- A
  $\dfrac{v}{4L}$
- B
  $\dfrac{v}{2L}$
- C
  $\dfrac{v}{L}$
- D
  $\dfrac{2v}{L}$
Closed pipe harmonics
$f_{n} = (2 n - 1) \frac{v}{4 L} (odd only)$
Q1MCQClosed pipe harmonics
A closed organ pipe produces which harmonics?
- A
  only odd harmonics
- B
  only even harmonics
- C
  all harmonics
- D
  none
Open pipe fundamental
$f = \frac{v}{2 L}$
Q1MCQOpen pipe
The fundamental frequency of an open organ pipe is:
- A
  $\dfrac{v}{2L}$
- B
  $\dfrac{v}{4L}$
- C
  $\dfrac{v}{L}$
- D
  $\dfrac{2v}{L}$
Open pipe harmonics
$f_{n} = n \frac{v}{2 L}$
Q1MCQOpen pipe harmonics
An open organ pipe produces which harmonics?
- A
  all harmonics
- B
  only odd
- C
  only even
- D
  none
Doppler (general)
$f^{'} = f \frac{v \pm v _{o}}{v \mp v _{s}}$
Q1MCQDoppler general
The Doppler-shifted frequency is:
- A
  $f\dfrac{v\pm v_o}{v\mp v_s}$
- B
  $f\dfrac{v_s}{v_o}$
- C
  $f(v_o-v_s)$
- D
  $f$
Doppler (source approaching)
$f^{'} = f \frac{v}{v - v _{s}}$
Q1MCQSource approaching
When a source approaches a stationary observer, the frequency is:
- A
  $f\dfrac{v}{v-v_s}$
- B
  $f\dfrac{v}{v+v_s}$
- C
  $f\dfrac{v+v_s}{v}$
- D
  $f$
Doppler (observer approaching)
$f^{'} = f \frac{v + v _{o}}{v}$
Q1MCQObserver approaching
When an observer approaches a stationary source, the frequency is:
- A
  $f\dfrac{v+v_o}{v}$
- B
  $f\dfrac{v}{v+v_o}$
- C
  $f\dfrac{v}{v-v_o}$
- D
  $f$
End correction (open pipe)
$f = \frac{v}{2 ( L + 0.6 d )}$
Q1MCQEnd correction
With end correction, an open pipe's frequency uses length:
- A
  $L+0.6d$
- B
  $L$
- C
  $L-0.6d$
- D
  $2L$
Resonance in a tube
$L = \frac{( 2 n - 1 ) λ}{4}$
Q1MCQTube resonance
Resonance in a closed tube occurs at lengths:
- A
  $\dfrac{(2n-1)\lambda}{4}$
- B
  $\dfrac{n\lambda}{2}$
- C
  $n\lambda$
- D
  $\dfrac{\lambda}{2}$
Loudness–intensity
$L \propto lo g I$
Q1MCQLoudness
Loudness of a sound depends on its intensity as:
- A
  $\log I$
- B
  $I$
- C
  $I^{2}$
- D
  $\dfrac{1}{I}$
Energy density of a wave
$u = 2 π^{2} f^{2} A^{2} ρ$
Q1MCQEnergy density
The energy density of a sound wave is proportional to:
- A
  $f^{2}A^{2}$
- B
  $fA$
- C
  $\dfrac{1}{A}$
- D
  $f$
Speed at 0°C vs T°C
$v_{T} = v_{0} \frac{T}{273}$
T in kelvin
Q1MCQSpeed vs T
If the temperature of air increases, the speed of sound:
- A
  increases
- B
  decreases
- C
  stays the same
- D
  becomes zero

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Sound Wave formulas

Sound Wave, every formula

Speed of sound (general)

Speed in a gas (Newton–Laplace)

Speed in a solid

Wave relation

Temperature dependence

Intensity

Intensity level (decibel)

Displacement wave

Pressure amplitude

Beats

Closed pipe fundamental

Closed pipe harmonics

Open pipe fundamental

Open pipe harmonics

Doppler (general)

Doppler (source approaching)

Doppler (observer approaching)

End correction (open pipe)

Resonance in a tube

Loudness–intensity

Energy density of a wave

Speed at 0°C vs T°C

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