Sound Waves and the Doppler Effect (4D) - Chem & Physics

1. If a source approaches a stationary observer, is the observed wavelength larger or smaller?

   Smaller wavelength (wavefronts are compressed). Source motion toward observer bunches wavefronts, reducing the effective wavelength.

2. What is the standard reference intensity $I_0$ for sound in air?

   $I_0 = 1\times 10^{-12}\ \text{W/m}^2$. Represents the threshold of human hearing, used as the baseline for decibel measurements.

3. What is the speed of sound in air at room temperature used for MCAT approximations?

   $v \approx 340\ \text{m/s}$. Approximates the speed of sound in dry air at 20°C, commonly used in MCAT problems for calculations.

4. What is the beat frequency for two close frequencies $f_1$ and $f_2$?

   $f_{\text{beat}} = |f_1 - f_2|$. Arises from interference of two waves, producing amplitude modulation at the difference frequency.

5. Which wave property primarily determines perceived loudness: amplitude or frequency?

   Amplitude (via intensity). Loudness correlates with the energy carried by the wave, which depends on amplitude through intensity.

6. What type of mechanical wave is sound in air (transverse or longitudinal)?

   Longitudinal mechanical wave. Sound propagates as compressions and rarefactions parallel to the direction of travel in fluids like air.

7. What is the relationship between intensity and amplitude for a sound wave?

   $I \propto A^2$. Energy in waves scales with the square of the amplitude, linking intensity to wave strength.

8. What is the definition of frequency for a periodic sound wave?

   Cycles per second; measured in Hz. Quantifies the number of wave cycles per unit time, with hertz as the SI unit.

9. What is the definition of intensity in terms of power and area?

   $I = \frac{P}{A}$. Defines sound intensity as the power transmitted per unit area perpendicular to the wave direction.

10. A $680\ \text{Hz}$ source recedes from a stationary observer at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

    $f' \approx 618\ \text{Hz}$. Source recession stretches waves, decreasing frequency by $v/(v + v_s) \approx 0.909$.

11. If distance from a point source doubles, what is the change in sound level (approx)?

    Decrease of $\approx 6\ \text{dB}$. Doubling distance quarters intensity ($1/4$), and $\log_{10}(1/4) = -0.6$, so subtracts 6 dB.

12. A siren emits $500\ \text{Hz}$; observer moves toward it at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

    $f' = 550\ \text{Hz}$. Observer motion increases relative speed, raising frequency by factor $(v + v_o)/v = 1.1$.

13. What is the definition of wavelength for a sound wave in a medium?

    Distance between successive compressions (or rarefactions). Measures the spatial period of the pressure variations in the propagating sound wave.

14. What is the Doppler formula for a moving source and stationary observer?

    $f' = f\left(\frac{v}{v \mp v_s}\right)$. Reflects changes in emitted wavelength due to source motion relative to the medium.

15. What is the general Doppler formula when both observer and source move in the medium?

    $f' = f\left(\frac{v \pm v_o}{v \mp v_s}\right)$. Combines effects of both source and observer velocities relative to the wave speed in the medium.

16. If intensity increases by a factor of $10$, how does the sound level change in dB?

    Increase of $10\ \text{dB}$. Logarithmic nature of decibels means a tenfold intensity increase corresponds to adding 10 dB.

17. If intensity doubles, what is the approximate change in sound level $\Delta\beta$?

    $\Delta\beta \approx 3\ \text{dB}$. Since $\log_{10}(2) \approx 0.3$, a factor of 2 in intensity adds about 3 dB to the sound level.

18. What is the definition of amplitude for a sound wave in a medium?

    Maximum pressure (or displacement) variation from equilibrium. Represents the peak deviation in pressure or particle displacement from the equilibrium state.

19. What is the Doppler formula for a moving observer and stationary source?

    $f' = f\left(\frac{v \pm v_o}{v}\right)$. Accounts for the relative speed of the observer affecting the rate of wavefront encounters.

20. What is the decibel level formula in terms of intensity ratio $I/I_0$?

    $\beta = 10\log_{10}\!\left(\frac{I}{I_0}\right)$. Calculates sound level in decibels using a logarithmic scale relative to the reference intensity.

21. What is the wave-speed relation connecting speed, frequency, and wavelength?

    $v = f\lambda$. Expresses the fundamental relationship for periodic waves where speed equals frequency times wavelength.

22. For a point source, how does sound intensity scale with distance $r$?

    $I \propto \frac{1}{r^2}$. Follows the inverse square law due to spherical spreading of energy from the source.

23. In Doppler sign convention, which sign gives higher observed frequency for approach?

    Use $+v_o$ and $-v_s$ (approach increases $f'$). Signs are chosen to increase numerator or decrease denominator when closing the distance.

24. Which wave property primarily determines perceived pitch: amplitude or frequency?

    Frequency. Human auditory system perceives higher frequencies as higher pitch in sound waves.

25. A $1000\ \text{Hz}$ source moves toward a stationary observer at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

    $f' \approx 1111\ \text{Hz}$. Source approach compresses waves, increasing frequency by $v/(v - v_s) \approx 1.111$.

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