Doppler effect | PhysicsRank

A passing siren changes pitch even when its source keeps vibrating at the same rate. What changes is the timing of arrivals at your ear. Counting wavefronts gives a more dependable explanation than choosing signs from memory.

We will derive each effect from that distinction. Source and receiver motion will be treated separately, beat-frequency ambiguities will be resolved with controlled changes, and sound levels will be calculated from intensities rather than added directly.

What you will learn to do

Derive source and receiver Doppler factors in the medium frame.
Use a signed one-dimensional formula and check approaching/receding limits.
Treat a moving-reflector echo as two frequency changes.
Explain why beat frequency is the full frequency difference.
Resolve an unknown-frequency ambiguity with a controlled adjustment.
Distinguish rms pressure, intensity and subjective loudness.
Combine incoherent sources and geometric spreading using decibel differences.

Useful before this chapterTravelling waves, superposition and energy →Exponential change, logarithms and controlled approximations →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

BEFORE YOU READ

Bring back one idea

Try a sentence or a sketch before opening the comparison. If this is new, use the explanation to get started.

What distinguishes the frequency emitted by a source from the frequency received by an observer?

Compare your reasoning

Emission frequency counts cycles produced per second at the source. Received frequency counts arrivals per second at the observer. Motion can alter the spacing or encounter rate of the wavefronts.

Revisit the explanation →

01 / Sound: Doppler shifts, beats and intensity levels

Frequency at a receiver counts arriving wavefronts

A source frequency tells us how many oscillations the source produces each second. A detected frequency counts how many wavefronts pass a receiver each second. Motion can change that arrival rate even when the source continues oscillating at a fixed frequency.

For sound, the medium provides a physical reference frame. The wave speed c is measured relative to the air or other medium. Source motion changes the spacing of wavefronts in that medium; receiver motion changes the rate at which the receiver meets them. These are different mechanisms and need not produce identical shifts for equal speeds.

Keep pitch, intensity and source distance separate. A source can get louder as it approaches because less spreading separates it from the receiver, while its detected frequency changes because of wavefront timing. Neither effect is the definition of the other.

The formulas here describe nonrelativistic sound in a uniform stationary medium, with collinear subsonic motions and steady frequencies. Light requires a relativistic treatment, and a source crossing the sound speed produces shock-wave geometry outside this elementary formula’s intended regime.

STOP & THINK

Why do sound-source speed and receiver speed enter different parts of the Doppler formula?

They change different things: wavefront spacing and encounter rate
Only source motion matters
Sound speed always increases when the source moves

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: Frequency at a receiver counts arriving wavefronts
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Back to chapter contents ↑

02 / Sound: Doppler shifts, beats and intensity levels

A moving source changes the emitted wavelength

Let the source emit successive crests a time T_s = 1/f_s apart. During that time, the first crest travels cT_s through the still medium. If the source moves toward a receiver at speed u_s, it advances u_sT_s before emitting the next crest. The forward spacing is therefore λ_front = (c − u_s)T_s.

A stationary receiver ahead of the source detects f_o = c/λ_front = f_sc/(c − u_s). A receding source leaves a larger spacing behind it, λ_back = (c + u_s)T_s, so the detected frequency is lower.

The source changes wavelength in the medium, not the medium’s wave speed. Using c + u_s as the propagation speed toward a stationary receiver would describe a different and incorrect model for sound in still air.

As a subsonic source speed approaches c in the ideal forward formula, the spacing becomes very small. This signals a singular limit in the simple geometry; it should not be used to describe a finite ordinary tone from a supersonic source by allowing a negative denominator.

\lambda_{\mathrm{front}}=\frac{c-u_s}{f_s},\qquad f_o=f_s\frac{c}{c-u_s}

Here u_s is positive for source motion toward a stationary receiver and u_s < c. For recession, replace c − u_s by c + u_s.

WORKED EXAMPLE

Derive a frequency from the compressed spacing

A source emits at 500 Hz while moving toward a stationary receiver at 30 m/s through still air. Take sound speed as 330 m/s. Find the wavelength ahead of the source and the received frequency.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: A moving source changes the emitted wavelength
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
\lambda_{\mathrm{front}}=\frac{c-u_s}{f_s},\qquad f_o=f_s\frac{c}{c-u_s}
Meaning: Here u_s is positive for source motion toward a stationary receiver and u_s < c. For recession, replace c − u_s by c + u_s.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

03 / Sound: Doppler shifts, beats and intensity levels

A moving receiver changes its encounter speed

A stationary source produces wavelength λ = c/f_s in the medium. If a receiver moves toward the incoming wavefronts at speed u_o, the closing speed between receiver and fronts is c + u_o. Its detected frequency is (c + u_o)/λ.

For the same numerical speed, a moving receiver and a moving source generally produce slightly different shifts. The receiver changes the numerator, while the source changes the wavelength and therefore the denominator. At speeds much smaller than c their first-order fractional shifts are similar, but the exact expressions are different.

For one-dimensional propagation toward positive x, define signed medium-frame velocities v_s and v_o positive along that direction. Then the wavelength between forward-emitted fronts is (c − v_s)/f_s, and their speed relative to the receiver is c − v_o. The combined result is f_o = f_s(c − v_o)/(c − v_s).

This signed convention avoids a collection of unrelated plus-or-minus choices. A receiver moving toward a source on its left has v_o < 0, which increases the numerator. A source approaching a receiver to its right has v_s > 0, which decreases the denominator. In each case the received frequency rises.

f_o=f_s\frac{c-v_o}{c-v_s}

The wave travels along positive x; both velocities are signed along that axis relative to the uniform medium. Source and receiver remain in the stated order during the interval considered.

WORKED EXAMPLE

Compare equal-speed source and receiver motions

A stationary 500 Hz source is heard by a receiver moving toward it at 30 m/s. Take c = 330 m/s. Compare the detected frequency with the 550 Hz obtained when the source approached a stationary receiver at the same speed.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

WORKED EXAMPLE

Test a case where both objects move

A source and receiver move in the same direction at the same constant velocity through still air, with the receiver ahead and their separation constant. What frequency does the receiver detect in the one-dimensional subsonic model?

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: A moving receiver changes its encounter speed
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
f_o=f_s\frac{c-v_o}{c-v_s}
Meaning: The wave travels along positive x; both velocities are signed along that axis relative to the uniform medium. Source and receiver remain in the stated order during the interval considered.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

04 / Sound: Doppler shifts, beats and intensity levels

A moving reflector produces two successive Doppler changes

An echo from a moving surface involves two stages. First the surface receives the incident sound at a shifted frequency. Then it acts as a moving source for the reflected wave. In the ideal nonrelativistic model, the reflected frequency equals the incident frequency in the reflector’s own frame.

For a stationary source and receiver at the same location, with a reflecting wall approaching at speed u through still air, the first shift multiplies frequency by (c + u)/c. The return wave is emitted by an approaching reflector, producing another factor c/(c − u). Their product is (c + u)/(c − u).

This reasoning assumes a reflector moving along the beam direction, a sufficiently steady signal and an ideal reflection. A moving object at an angle requires the velocity components along the relevant propagation directions. Do not simply double a speed inside a single-source formula.

A useful small-speed check is f_echo/f ≈ 1 + 2u/c when u ≪ c. The factor two arises from two stages of wavefront timing, not from a literal propagation speed of c + 2u.

WORKED EXAMPLE

Apply the two stages rather than guessing a sign

A stationary transmitter and receiver emit an 800 Hz tone toward a large wall approaching at 20 m/s. Take c = 340 m/s and ideal normal reflection. Find the echo frequency.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: A moving reflector produces two successive Doppler changes
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

05 / Sound: Doppler shifts, beats and intensity levels

Nearby frequencies create a slowly varying interference pattern

At one observation point, add two equal-amplitude oscillations A cos(2πf₁t) and A cos(2πf₂t). A trigonometric identity writes their sum as a rapid oscillation near the mean frequency multiplied by a slowly varying envelope.

The signed envelope is 2A cos[π(f₁ − f₂)t]. Its magnitude determines the oscillation amplitude, so both positive and negative envelope extrema produce loudness maxima. The maxima repeat at the difference frequency |f₁ − f₂|, not half that value.

The phases drift because the two frequencies are different. At some times the oscillations reinforce and at others they oppose. If the received amplitudes are unequal, the minima do not reach zero: their smallest resultant amplitude is |A₁ − A₂|.

The familiar perception of slow beats requires a sufficiently small frequency difference and comparable received amplitudes. For a large difference, the sound need not be perceived as a single tone with slowly varying loudness, even though the mathematical superposition remains valid.

y=2A\cos\!\big[\pi(f_1-f_2)t\big]\cos\!\big[\pi(f_1+f_2)t\big],\qquad f_{\mathrm{beat}}=|f_1-f_2|

The amplitude envelope is the absolute value of the first factor. Counting maxima of the signed cosine alone would miss alternate beats.

Count beat maxima

Inspect a plotted point: time (s) = 0

Cycle-averaged intensity: 4

For two equal received amplitudes at 450 Hz and 456 Hz, the rapid carrier is averaged out here. The plotted intensity relative to one tone is 2 + 2 cos(2π·6t), giving three beat intervals in half a second. Lines connect the plotted samples.

WORKED EXAMPLE

Distinguish the envelope sign from observable beat repetition

Two steady tones at 450 Hz and 456 Hz arrive with equal amplitudes. Find the beat frequency and the interval between neighbouring intensity maxima.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: Nearby frequencies create a slowly varying interference pattern
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
y=2A\cos\!\big[\pi(f_1-f_2)t\big]\cos\!\big[\pi(f_1+f_2)t\big],\qquad f_{\mathrm{beat}}=|f_1-f_2|
Meaning: The amplitude envelope is the absolute value of the first factor. Counting maxima of the signed cosine alone would miss alternate beats.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

06 / Sound: Doppler shifts, beats and intensity levels

A beat count usually leaves two possible unknown frequencies

If an unknown tone produces b beats per second with a known frequency f₀, its frequency could be f₀ + b or f₀ − b. A beat count alone does not tell which side of the reference it lies on.

A controlled change can resolve the ambiguity. If the unknown frequency is reduced by a known small amount and the beat frequency decreases without crossing the reference, the original unknown was above the reference. If the beat frequency increases, it was below.

Be cautious with qualitative tuning changes. Adding a small mass to a tuning-fork prong generally lowers its natural frequency in the elementary loading picture, while increasing tension in an ideal fixed-length string raises its frequency. State the physical effect of the adjustment instead of assuming all changes act the same way.

Beat measurements can detect small frequency differences accurately, but source drift and changing relative amplitudes can make counting unreliable. Record several beat intervals and maintain a stable reference. A moving source can itself create a frequency shift, so motion must be controlled when using beats for calibration.

WORKED EXAMPLE

Resolve the higher-or-lower ambiguity

An unknown steady tone produces 4 beats/s with a 300 Hz reference. A controlled adjustment lowers the unknown frequency by exactly 1 Hz, after which 3 beats/s are observed. Find the original unknown frequency.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

STOP & THINK

Two nearby-frequency tones have received amplitudes 3A and A. What is the ratio of maximum to minimum cycle-averaged intensity?

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: A beat count usually leaves two possible unknown frequencies
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

07 / Sound: Doppler shifts, beats and intensity levels

Intensity measures energy flow, not perceived loudness

Sound intensity is average power crossing a unit area perpendicular to propagation. Its SI unit is W/m². A source’s acoustic power is a total rate of energy emission; intensity also depends on how that power is distributed through space.

For an isotropic point source in an unbounded medium without absorption, I = P/(4πr²). Doubling distance reduces intensity by four. Directional sources, reflections, near-field structure and absorption can all invalidate this simple inverse-square model.

For a small-amplitude plane travelling sound wave in a uniform fluid, intensity can be expressed through pressure: I = p_rms²/(ρc) = p_peak²/(2ρc). The distinction between rms and peak introduces a factor of two. This expression relates the pressure and particle velocity of a travelling wave; a standing wave requires attention to their phase and net energy flow.

Perceived loudness depends on frequency, listener and other factors. A physical intensity ratio is therefore not automatically the same numerical ratio of subjective loudness. We use intensity level next as a logarithmic physical quantity with a specified reference.

I=\frac{p_{\mathrm{rms}}^2}{\rho c}=\frac{p_{\mathrm{peak}}^2}{2\rho c}

The pressure expressions assume a sinusoidal plane travelling wave in a medium of acoustic impedance ρc.

WORKED EXAMPLE

Keep rms pressure distinct from peak pressure

A plane travelling sound wave has rms pressure 0.20 Pa in a model medium with density 1.25 kg/m³ and sound speed 320 m/s. Find its intensity.

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: Intensity measures energy flow, not perceived loudness
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
I=\frac{p_{\mathrm{rms}}^2}{\rho c}=\frac{p_{\mathrm{peak}}^2}{2\rho c}
Meaning: The pressure expressions assume a sinusoidal plane travelling wave in a medium of acoustic impedance ρc.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

08 / Sound: Doppler shifts, beats and intensity levels

A logarithmic level turns intensity ratios into differences

Define sound intensity level β = 10 log₁₀(I/I₀), expressed in decibels. In the usual airborne-sound convention used here, I₀ = 10⁻¹² W/m². The logarithm acts on a dimensionless ratio, so a level cannot be calculated from a dimensional intensity without naming a reference.

Subtracting two levels gives Δβ = 10 log₁₀(I₂/I₁). A tenfold intensity increase adds 10 dB, a hundredfold increase adds 20 dB and a doubling adds about 3.01 dB. A negative level means intensity below the chosen reference, not negative physical intensity.

For incoherent sources at the same observation point, add intensities first and then take the logarithm. Two equal sources each producing level β give β + 10 log₁₀2, not 2β. Coherent sources can interfere, so their phase relationship must be considered before using an intensity sum.

If the same medium’s travelling-wave relation applies, an rms pressure ratio gives Δβ = 20 log₁₀(p₂/p₁), because intensity is proportional to pressure squared. The coefficient 20 belongs to an amplitude ratio under that relation, not to an arbitrary intensity ratio.

\beta=10\log_{10}\!\left(\frac{I}{I_0}\right),\qquad\Delta\beta=10\log_{10}\!\left(\frac{I_2}{I_1}\right)

Use I₀ = 10⁻¹² W/m² for the intensity-level calculations in this chapter. Differences do not depend on the numerical reference if the same reference is used.

WORKED EXAMPLE

Combine equal incoherent sources correctly

One source produces intensity level 60 dB at a point. Three more independent incoherent sources are added, each producing the same intensity there. What total intensity level results?

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

WORKED EXAMPLE

Translate geometric spreading into a level change

An ideal isotropic point source is observed first at distance r and then at 3r, with no absorption or reflections. What change in intensity level follows?

MEMBERSThe approach, step-by-step working and check are for members.Unlock →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Sound: Doppler shifts, beats and intensity levels
Focus: A logarithmic level turns intensity ratios into differences
Learning goals:
- Derive source and receiver Doppler factors in the medium frame.
- Use a signed one-dimensional formula and check approaching/receding limits.
- Treat a moving-reflector echo as two frequency changes.
- Explain why beat frequency is the full frequency difference.
- Resolve an unknown-frequency ambiguity with a controlled adjustment.
- Distinguish rms pressure, intensity and subjective loudness.
- Combine incoherent sources and geometric spreading using decibel differences.
Equations in this section (LaTeX):
\beta=10\log_{10}\!\left(\frac{I}{I_0}\right),\qquad\Delta\beta=10\log_{10}\!\left(\frac{I_2}{I_1}\right)
Meaning: Use I₀ = 10⁻¹² W/m² for the intensity-level calculations in this chapter. Differences do not depend on the numerical reference if the same reference is used.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

BRING THE IDEAS TOGETHER

What should stay with you

Sound-source motion changes wavelength; receiver motion changes encounter rate.
The sound formulas use velocities relative to the medium.
A moving-reflector echo requires two Doppler stages.
Beat frequency is |f₁ − f₂|, while a beat count alone leaves two frequency candidates.
Unequal received amplitudes produce nonzero beat minima.
Add incoherent intensities before converting to decibels.
A negative intensity level does not mean negative intensity.

RETRIEVE, THEN EXPLAIN

Try it without the examples

Work these out before checking. If an answer surprises you, identify which assumption or step needs another look. A correct choice is most useful when you can explain why the alternatives fail.

SELF CHECK 1

Two received tones have frequencies 512 Hz and 507 Hz. What is their beat frequency?

Answer in Hz.

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

SELF CHECK 2

An intensity increases by a factor of 100. By how many decibels does its intensity level increase?

Answer in dB.

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

SELF CHECK 3

A 600 Hz source approaches a stationary receiver at 20 m/s in still air with c = 320 m/s. What frequency is detected?

Answer in Hz.

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

SELF CHECK 4

Two equal incoherent sources each produce 50 dB at a point. Their combined level is approximately what?

100 dB
53 dB
50 dB

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

SELF CHECK 5

A tone gives 2 beats/s with a 400 Hz reference. Can the unknown frequency be determined uniquely from this alone?

Yes, it must be 402 Hz
Yes, it must be 398 Hz
No, either 398 Hz or 402 Hz is possible

MEMBERSAnswer checking, feedback and the explanation are for members.Unlock →

APPLY THE CHAPTER

Take the ideas into a problem

Try a complete problem next. Commit to a method before revealing a hint, then compare your reasoning with the worked solution.

Add intensities before decibelsIntermediate · Hints and guided reasoning A slow envelope from two nearby tonesIntermediate · Hints and guided reasoning A moving source compresses wavefrontsIntermediate · Hints and guided reasoning

COME BACK TO THE IDEA

What can you explain later?

Try these from memory at your next study session, then again a few days later. Say your reasoning aloud or sketch it before looking. Adjust the gap to what you can explain.

Next study session

A sound source approaches a stationary observer through still air. Why is the wavelength in front of it shorter?

Compare your reasoning

The source advances between successive emissions, so adjacent wavefronts are launched closer together in front. Their speed through the air is set by the medium in this model.

Revisit the explanation →

A few days later: change the situation

Two nearby tones make beats. If the beat rate falls when one tone is raised slightly, what can you infer before the frequencies cross?

Compare your reasoning

The adjusted tone was the lower-frequency one: raising it reduced their frequency difference. Beat rate alone gives a difference magnitude, so the direction of change supplies the missing ordering information.

Revisit the explanation →

Compare the physical reason, the assumptions and the conclusion. Your wording can differ. If one part is missing, revisit that section and try explaining it again after a break.

Back to chapter contents ↑