πSound Waves
Sound as a Longitudinal Wave
Sound is a longitudinal mechanical wave β molecules vibrate back and forth in the same direction the wave travels, creating regions of compression (high pressure) and rarefaction (low pressure).
Properties of sound: - Speed depends on medium: faster in denser/stiffer materials - Air: ~343 m/s at 20Β°C - Water: ~1500 m/s - Steel: ~5000 m/s
- Frequency determines pitch: higher frequency = higher pitch - Amplitude determines loudness: larger amplitude = louder sound
Sound can't travel through a vacuum (no medium = no wave).
The Doppler Effect
The Doppler effect is the change in observed frequency when the source and observer are moving relative to each other.
- Source moving TOWARD observer: observed frequency is HIGHER (pitch goes up) - Source moving AWAY from observer: observed frequency is LOWER (pitch goes down)
Classic example: an ambulance siren. As it approaches, the pitch sounds higher; as it passes and moves away, the pitch drops.
The formula (AP Physics 1 level β understand the concept, not usually required to calculate): f_observed = f_source Γ (v Β± v_observer)/(v β v_source)
Where + signs apply when approaching, β when receding.
Think About It
Explain the Doppler effect in terms of what happens to the wavefronts. Why does an approaching source seem to have higher frequency?
βοΈ Worked Example
Problem: Two speakers emit the same 440 Hz sound. You walk toward Speaker A and away from Speaker B. Do you hear a beat frequency? Explain.
π Key Equations
Sound and Doppler
v_sound β 343 m/s (air, 20Β°C)f_observed = f_s\fracv Β± v_obsv β v_sf_beat = |f_1 - f_2|β οΈ Common Mistakes
Misconception: Sound travels faster through less dense media.
β Correct thinking: Sound travels faster through stiffer (higher bulk modulus) media. Denser materials can be slower or faster depending on their stiffness β steel is denser than air yet much faster.
Why: Speed = β(stiffness/density). Steel's enormous stiffness more than compensates for its density, giving ~5000 m/s vs. 343 m/s in air.
Misconception: When a source moves toward you, the sound waves travel faster.
β Correct thinking: The wave speed in the medium stays the same. The Doppler effect changes the frequency and wavelength, not the speed.
Why: Wave speed is set by the medium (air, water, etc.), not by the motion of the source. Motion compresses or stretches the wavefronts, changing Ξ» and f.
Misconception: Beats only occur when two sounds have very different frequencies.
β Correct thinking: Beats occur most noticeably when frequencies are very CLOSE together. The beat frequency equals the difference: f_beat = |fβ β fβ|.
Why: If the frequencies are far apart, the beat frequency is too fast to hear as a distinct pulse. Beats are only perceptible when f_beat is roughly 1β20 Hz.
π Practice Problems
Try these problems. Check your answer when ready.
Two tuning forks vibrate at 440 Hz and 444 Hz simultaneously. What beat frequency do you hear?
A siren emits 600 Hz. You are stationary and the siren moves toward you at 34 m/s. What frequency do you hear? (v_sound = 340 m/s)
f_obs = f_s Β· (v)/(v - v_s)You are moving toward a stationary 500 Hz source at 17 m/s. What frequency do you hear? (v_sound = 340 m/s)
f_obs = f_s Β· \fracv + v_obsvA bat emits 50,000 Hz ultrasound and detects the echo at 51,000 Hz from an insect. Is the insect moving toward or away from the bat? Explain.
Explain why you can hear sound around corners but not see light around corners.
A source emits 800 Hz and moves away from a stationary observer at 85 m/s (v_sound = 340 m/s). Simultaneously, the observer moves toward the source at 17 m/s. What frequency does the observer hear?
f_obs = f_s Β· \fracv + v_obsv + v_sFinished reading through this lesson?