PHSX 220 Physics I (w/ Calculus) · Unit 4: Oscillations, waves, sound · on Final (Exam 4)
Ch 17 Sound
Study notes for Sound in PHSX 220 Physics I (w/ Calculus) at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in Mathub.
Big ideas
- Sound is a longitudinal pressure wave. Speed in air about 343 m/s at 20 °C (rises with temperature); much faster in water and solids. $v = f\lambda$ still.
- Intensity $I = P/A$ (W/m²) falls off as $1/r^2$ from a point source. Sound level in decibels: $\beta = 10\log_{10}(I/I_0)$ with $I_0 = 10^{-12}\ \text{W/m}^2$. Every $+10$ dB is $\times10$ intensity; $+3$ dB is about $\times2$.
- Pipes: open–open resonates at $f_n = n\dfrac{v}{2L}$ (all harmonics); closed–open at $f_n = n\dfrac{v}{4L}$ with odd $n$ only.
- Beats: two close frequencies produce a loudness wobble at $f_{\text{beat}} = |f_1 - f_2|$.
- Doppler effect: $f' = f\dfrac{v \pm v_o}{v \mp v_s}$. Top signs for approach (observer toward source: $+v_o$; source toward observer: $-v_s$). Approaching raises pitch.
Key formulas
Intensity and decibels
$$I = \frac{P}{4\pi r^2},\qquad \beta = 10\log_{10}\frac{I}{I_0},\qquad I_0 = 10^{-12}\ \text{W/m}^2$$
Pipes and beats
$$f_n = n\frac{v}{2L}\ \text{(open)},\quad f_n = n\frac{v}{4L},\ n\ \text{odd (closed)},\quad f_{\text{beat}} = |f_1 - f_2|$$
Doppler
$$f' = f\,\frac{v \pm v_o}{v \mp v_s}$$
Worked example
An ambulance siren at 700 Hz approaches a stationary listener at 30 m/s (air: 343 m/s). What frequency is heard? What after it passes?
Show the solution
Approaching: $f' = 700\cdot\frac{343}{343-30} = 767$ Hz. Receding: $700\cdot\frac{343}{343+30} = 644$ Hz.
Common mistakes
- Mixing up which speed goes in the numerator (observer) and denominator (source).
- Doubling intensity and expecting 10 dB more (it is 3 dB).
- Using even harmonics for a closed pipe.
Exam tipFor Doppler, decide physically first: approaching means higher pitch. Then pick the signs that make the fraction move that way.
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