Medium MCAT Waves and Sound Practice Questions

Mastering waves and sound is a critical component of the Chemical and Physical Foundations of Biological Systems section of the MCAT. This guide provides Medium MCAT Waves and Sound Practice Questions designed to bridge the gap between basic definitions and the complex application of physical principles in biological contexts. By working through these problems, you will sharpen your ability to calculate frequencies, intensities, and Doppler shifts—skills essential for scoring high on the physics portion of the exam.

Concept Explanation

Waves and sound involve the transfer of energy through a medium via oscillations, categorized primarily as transverse or longitudinal waves. In physics, a wave is a disturbance that travels through space and matter, transferring energy from one point to another without the permanent displacement of the medium itself. For the MCAT, you must distinguish between mechanical waves (like sound), which require a medium, and electromagnetic waves, which can travel through a vacuum. Sound is a longitudinal mechanical wave characterized by regions of compression and rarefaction. Key parameters include wavelength $\lambda$, frequency $f$, amplitude, and period $T$, related by the fundamental wave equation:

$$v = f\lambda$$

Understanding sound also requires knowledge of intensity (measured in decibels), the Doppler Effect, and standing waves in pipes and strings. For instance, the Doppler Effect explains the perceived change in frequency when a source and observer move relative to one another. These concepts are frequently tested in medical contexts, such as the physics behind ultrasound imaging or the human ear's perception of pitch. Just as you might study Medium MCAT General Chemistry Practice Questions to master stoichiometry, mastering wave mechanics requires repetitive practice with varying mathematical constraints.

Solved Examples

The following examples demonstrate how to apply wave formulas to typical MCAT-style problems.

1. Calculating Wave Speed: A sound wave with a frequency of 440 Hz travels through a medium with a wavelength of 0.75 meters. What is the speed of the sound wave?
   1. Identify the given values: $f = 440 \text{ Hz}$ and $\lambda = 0.75 \text{ m}$.
   2. Use the wave equation: $v = f\lambda$.
   3. Substitute the values: $v = 440 \times 0.75$.
   4. Calculate the result: $v = 330 \text{ m/s}$.
2. Doppler Effect (Approaching Source): An ambulance siren emits a sound at 1000 Hz. If the ambulance moves toward a stationary observer at 20 m/s, what frequency does the observer hear? (Assume the speed of sound is 340 m/s).
   1. Use the Doppler formula: $f' = f \frac{v \pm v_d}{v \mp v_s}$.
   2. Since the observer is stationary, $v_d = 0$. Since the source is moving toward the observer, use the minus sign in the denominator: $f' = 1000 \frac{340}{340 - 20}$.
   3. Simplify: $f' = 1000 \frac{340}{320} = 1000 \times 1.0625$.
   4. Result: $f' = 1062.5 \text{ Hz}$.
3. Intensity Change: If the intensity of a sound is increased by a factor of 100, by how many decibels does the sound level increase?
   1. Recall the decibel formula: $\beta = 10 \log \frac{I}{I_0}$.
   2. The change in sound level is $\Delta \beta = 10 \log \frac{I_{final}}{I_{initial}}$.
   3. Substitute the factor of 100: $\Delta \beta = 10 \log(100)$.
   4. Since $\log(100) = 2$, the calculation is $10 \times 2 = 20 \text{ dB}$.

Practice Questions

Test your knowledge with these Medium MCAT Waves and Sound Practice Questions. Ensure you can manipulate variables without a calculator, as required on the actual exam.

1. A string of length 2.0 meters is fixed at both ends and vibrating in its third harmonic. What is the wavelength of the standing wave produced?

2. An ultrasound technician uses a probe emitting a frequency of 5 MHz. If the speed of sound in human tissue is approximately 1540 m/s, what is the wavelength of the ultrasound wave?

3. Two sound waves interfere constructively at a point. If wave A has an amplitude of 3 units and wave B has an amplitude of 4 units, what is the resulting amplitude at that point?

4. A pipe open at one end and closed at the other has a fundamental frequency of 100 Hz. What is the frequency of the next available harmonic (the 3rd harmonic)?

5. If the distance from a point source of sound is tripled, by what factor does the intensity of the sound change?

6. A sound wave transitions from air into water. Which of the following properties remains constant: speed, wavelength, or frequency?

7. A listener moves away from a stationary speaker at 10 m/s. If the speaker emits a 500 Hz tone and the speed of sound is 340 m/s, what frequency is perceived by the listener?

8. A wave on a rope has a period of 0.2 seconds and a wavelength of 0.5 meters. Calculate the speed of the wave.

9. A 60 dB sound is compared to a 30 dB sound. How many times more intense is the 60 dB sound?

10. What is the beat frequency produced by two tuning forks vibrating at 256 Hz and 260 Hz respectively?

Answers & Explanations

• Question 1: The formula for the harmonic of a string fixed at both ends is $\lambda = \frac{2L}{n}$. For the third harmonic ($n=3$) and $L=2.0 \text{ m}$, $\lambda = \frac{2 \times 2.0}{3} = 1.33 \text{ m}$.
• Question 2: Using $\lambda = \frac{v}{f}$, substitute $v = 1540 \text{ m/s}$ and $f = 5 \times 10^6 \text{ Hz}$. $\lambda = \frac{1540}{5 \times 10^6} = 308 \times 10^{-6} \text{ m}$ or $0.308 \text{ mm}$.
• Question 3: During constructive interference, amplitudes add together. $3 + 4 = 7 \text{ units}$.
• Question 4: For a pipe closed at one end, only odd harmonics exist ($n=1, 3, 5...$). The frequency of the $n$-th harmonic is $f_n = n \times f_1$. Thus, $f_3 = 3 \times 100 \text{ Hz} = 300 \text{ Hz}$.
• Question 5: Intensity follows the inverse square law: $I \propto \frac{1}{r^2}$. If distance $r$ is tripled, intensity becomes $\frac{1}{3^2} = \frac{1}{9}$ of the original.
• Question 6: When a wave changes media, its frequency remains constant because it is determined by the source. Speed and wavelength change according to the medium's properties.
• Question 7: Using the Doppler formula $f' = f \frac{v - v_d}{v}$ (minus because moving away): $f' = 500 \frac{340 - 10}{340} = 500 \frac{330}{340} \approx 485.3 \text{ Hz}$.
• Question 8: Frequency $f = \frac{1}{T} = \frac{1}{0.2} = 5 \text{ Hz}$. Speed $v = f\lambda = 5 \times 0.5 = 2.5 \text{ m/s}$.
• Question 9: The difference is $60 - 30 = 30 \text{ dB}$. Since every 10 dB represents a factor of 10 in intensity, 30 dB is $10^3 = 1000$ times more intense.
• Question 10: Beat frequency is the absolute difference between frequencies: $|260 - 256| = 4 \text{ Hz}$.

Quick Quiz

Frequently Asked Questions

What is the difference between transverse and longitudinal waves?

Transverse waves have oscillations perpendicular to the direction of energy transfer, while longitudinal waves have oscillations parallel to the direction of travel. Light is transverse, whereas sound is longitudinal.

How does temperature affect the speed of sound in air?

The speed of sound in air increases with temperature because molecules move faster and collide more frequently, allowing the disturbance to propagate more quickly. This is often modeled by the equation $v \approx 331 + 0.6T$, where $T$ is in Celsius.

Why can't sound travel through a vacuum?

Sound is a mechanical wave that requires a physical medium (gas, liquid, or solid) to transmit energy through particle collisions. Since a vacuum lacks matter, there are no particles to vibrate and carry the wave.

What is the significance of the threshold of hearing?

The threshold of hearing, $I_0 = 10^{-12} \text{ W/m}^2$, is the minimum intensity required for the average human ear to detect a sound at 1000 Hz. It serves as the reference point for the decibel scale.

How do harmonics differ between open and closed pipes?

Pipes open at both ends support all integer harmonics ($n=1, 2, 3...$), while pipes closed at one end only support odd harmonics ($n=1, 3, 5...$). This difference significantly affects the timbre and resonant frequencies of musical instruments.

For more practice with physical sciences, explore our Medium MCAT Electrochemistry Practice Questions or dive into organic chemistry with Medium MCAT Organic Chemistry Practice Questions.

Enjoyed this article?

Share it with others who might find it helpful.

Share Article