MCAT sound and Doppler effect cheat sheet

What is the speed of sound in air?

Approximately 343 m/s (1235 km/h or 767 mph) at 20°C (68°F).

Frequency and wavelength relationship.

The speed of sound $\displaystyle v = f imes \\lambda$, where $\displaystyle v$ is speed, $\displaystyle f$ is frequency, and $\displaystyle \\lambda$ is wavelength.

True or False: Sound waves are longitudinal.

True. Sound waves are longitudinal waves, meaning particle displacement is parallel to wave propagation.

What is pitch?

Pitch is the perceived frequency of a sound; higher frequency means higher pitch.

Define amplitude in sound waves.

Amplitude is the maximum displacement of particles from their equilibrium position; relates to loudness.

How does temperature affect sound speed?

Sound speed increases with temperature. Approximately $\displaystyle 0.6 \\text{m/s}$ increase per °C.

Fill in the blank: Sound requires a _____ to propagate.

Medium (solid, liquid, or gas).

What is the range of human hearing?

Typically from 20 Hz to 20,000 Hz (20 kHz).

Difference between constructive and destructive interference.

Constructive: waves add together; Destructive: waves cancel each other.

What is a decibel (dB)?

A logarithmic unit measuring sound intensity; a change of 10 dB represents a tenfold increase.

Example of resonance in sound.

A swing being pushed at its natural frequency increases amplitude; similarly for musical instruments.

Define sound intensity.

Sound intensity is the power per unit area; measured in watts per square meter (W/m²).

What is a standing wave?

A wave pattern formed by the interference of two traveling waves moving in opposite directions.

Cause → Effect: What happens to sound in a vacuum?

Sound cannot travel; there is no medium for propagation.

What is the formula for frequency?

Frequency $\displaystyle f = \frac{v}{\\lambda}$, where $\displaystyle v$ is speed and $\displaystyle \\lambda$ is wavelength.

True or False: Sound travels faster in solids than liquids.

True. Sound travels faster in solids due to closer particle packing.

What is the Doppler Effect?

The change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the waves.

Formula for observed frequency when source approaches observer?

The formula is: $\displaystyle f' = f \\frac{v + v_o}{v - v_s}$, where $\displaystyle f'$ is the observed frequency, $\displaystyle f$ is the source frequency, $\displaystyle v$ is the speed of sound, $\displaystyle v_o$ is the observer's speed, and $\displaystyle v_s$ is the source's speed.

True or False: The Doppler Effect applies only to sound waves.

False. The Doppler Effect applies to all types of waves, including light and electromagnetic waves.

Effect of moving away from sound source?

The observed frequency decreases due to the Doppler Effect as the source moves away. Formula: $\displaystyle f' = f \\frac{v - v_o}{v + v_s}$.

Fill in the blank: As the source approaches, the sound frequency _____

increases.

How does the Doppler Effect explain a passing siren?

As the ambulance approaches, the frequency sounds higher. As it moves away, the frequency sounds lower.

What is redshift?

A phenomenon where light from an object moving away is shifted to longer wavelengths. Key in astronomy to determine distance and motion.

Formula for wavelength change in Doppler Effect?

$\displaystyle \lambda' = \lambda \\frac{v \pm v_o}{v \mp v_s}$, where $\displaystyle \lambda'$ is the observed wavelength and $\displaystyle \lambda$ is the source wavelength.

Difference between blue shift and red shift?

Blue shift occurs when the object approaches (shorter wavelengths), while red shift occurs when it recedes (longer wavelengths).

What happens to frequency if both source and observer move towards each other?

The frequency increases more than if only the source was moving towards the observer due to both speeds contributing.

In astrophysics, what does Doppler effect indicate?

It indicates whether an object is moving towards or away from the observer, allowing for velocity measurements of celestial bodies.

Observed frequency when source moves away?

Formula: $\displaystyle f' = f \\frac{v - v_o}{v + v_s}$. Frequency decreases.

When is the Doppler effect maximal?

When the relative speed between the source and observer is at its highest.

True or False: The speed of sound is constant regardless of temperature.

False. The speed of sound increases with temperature; at 32°F, it's about 1,125 ft/s.

If an observer is stationary and the source approaches, frequency changes how?

It increases. The waves get compressed as the source moves closer.

Application of Doppler Effect in radar?

Used to measure the speed of moving objects by analyzing frequency shifts in radio waves reflected off them.

Calculate observed frequency: Source frequency 500 Hz, source speed 30 m/s, observer speed 10 m/s, sound speed 343 m/s.

Using formula: $\displaystyle f' = 500 \\frac{343 + 10}{343 - 30} \approx 520.5 Hz$.

What is the significance of Doppler effect in medical imaging?

It is used in ultrasound to measure blood flow and speed, aiding in diagnostics.

Calculate observed frequency: 1000 Hz, source speed 20 m/s, observer speed 5 m/s.

Use the formula: \( f' = f \\frac{v + v_0}{v - v_s} \) \( f' = 1000 \\frac{343 + 5}{343 - 20} \approx 1049.67 Hz \)

True or False: The Doppler Effect applies to light waves as well.

True. - Applies to any wave: sound, light, water. - Used in astronomy for redshift and blueshift.