MCAT Chemical and Physical Foundations of Biological Systems Flashcards: 4d Sound Waves Doppler Effect

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This deck focuses on 4d Sound Waves Doppler Effect, giving you a quick way to review the definitions, rules, and examples that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the standard reference intensity $I_0$ for sound in air?

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

Flashcard 2: What is the decibel level formula in terms of intensity ratio $I/I_0$?

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

Flashcard 3: For a point source, how does sound intensity scale with distance $r$?

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

Flashcard 4: Which wave property primarily determines perceived loudness: amplitude or frequency?

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

Flashcard 5: What is the definition of intensity in terms of power and area?

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

Flashcard 6: Which wave property primarily determines perceived pitch: amplitude or frequency?

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

Flashcard 7: What is the definition of amplitude for a sound wave in a medium?

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

Flashcard 8: A $680\ \text{Hz}$ source recedes from a stationary observer at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

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

Flashcard 9: A $1000\ \text{Hz}$ source moves toward a stationary observer at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

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

Flashcard 10: A siren emits $500\ \text{Hz}$; observer moves toward it at $34\ \text{m/s}$. Find $f'$ with $v=340\ \text{m/s}$.

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

Flashcard 11: What is the wave-speed relation connecting speed, frequency, and wavelength?

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

Flashcard 12: What is the speed of sound in air at room temperature used for MCAT approximations?

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

Flashcard 13: What type of mechanical wave is sound in air (transverse or longitudinal)?

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

Flashcard 14: If a source approaches a stationary observer, is the observed wavelength larger or smaller?

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

Flashcard 15: In Doppler sign convention, which sign gives higher observed frequency for approach?

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

Flashcard 16: What is the general Doppler formula when both observer and source move in the medium?

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

Flashcard 17: What is the Doppler formula for a moving source and stationary observer?

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

Flashcard 18: What is the Doppler formula for a moving observer and stationary source?

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

Flashcard 19: What is the beat frequency for two close frequencies $f_1$ and $f_2$?

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

Flashcard 20: What is the relationship between intensity and amplitude for a sound wave?

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

Flashcard 21: If distance from a point source doubles, what is the change in sound level (approx)?

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

Flashcard 22: If intensity doubles, what is the approximate change in sound level $\Delta\beta$?

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

Flashcard 23: What is the definition of frequency for a periodic sound wave?

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

Flashcard 24: What is the definition of wavelength for a sound wave in a medium?

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

Flashcard 25: If intensity increases by a factor of $10$, how does the sound level change in dB?

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