How waves carry sound, why echoes happen and what pitch, loudness and resonance really mean.
Sound is a longitudinal mechanical wave, so it needs a medium. Speed, frequency and wavelength are linked by v = f × λ. We take the speed of sound in air as 330 m/s.
A tuning fork vibrates at 440 Hz. Find the wavelength of its sound in air (v = 330 m/s).
λ = v/f = 330/440 = 0.75 m.
Find the time period of a source of frequency 50 Hz.
T = 1/f = 1/50 = 0.02 s.
The same 440 Hz note enters water where sound moves at 1500 m/s. Does the frequency change? Find the new wavelength.
Frequency does not change, because it is set by the source. λ = 1500/440 = 3.41 m, so the wavelength is larger.
An echo is heard when reflected sound reaches the ear at least 0.1 s after the original, because the ear keeps an impression of a sound for about 0.1 s. Echo problems use d = v × t / 2, as the sound travels to the wall and back.
Find the minimum distance to a wall to hear a clear echo when the sound speed is 330 m/s.
Sound must take at least 0.1 s for the round trip. d = 330 × 0.1 / 2 = 16.5 m.
A person hears the echo of a clap 2 s after clapping. How far is the cliff?
d = v t / 2 = 330 × 2 / 2 = 330 m.
A ship sends an ultrasonic pulse and receives the echo after 0.8 s. Sound speed in sea water is 1500 m/s. Find the depth of the sea bed.
Depth = 1500 × 0.8 / 2 = 600 m. This is the principle of SONAR.
Loudness depends on amplitude, pitch on frequency, and quality (timbre) on the waveform, which is why a flute and a violin differ on the same note. Humans hear about 20 Hz to 20,000 Hz. Free vibrations occur at the natural frequency; forced vibrations are caused by an external periodic force; damped vibrations lose amplitude with time. Resonance is a forced vibration at the natural frequency, giving a large amplitude.
Sound A has twice the amplitude of sound B at the same frequency. How do they differ?
A is louder; the pitch is the same, since frequency is unchanged.
Why can a singer break a glass with a high note?
If her note matches the glass's natural frequency, the glass resonates, the amplitude grows, and it can shatter.
Name the characteristic that lets you tell the same note played on a sitar and a guitar.
Quality (timbre), which depends on the waveform.
1. State the relation between speed, frequency and wavelength.
2. A wave has f = 220 Hz and v = 330 m/s. Find λ.
3. Why can sound not travel through a vacuum?
4. Define echo. What is its minimum time gap?
5. An echo returns after 1.5 s. Find the distance of the reflector (330 m/s).
6. Name two uses of echo or SONAR.
7. What does pitch depend on?
8. What are the audible limits of the human ear?
9. Distinguish free, forced and damped vibrations in one line each.
10. What is resonance? Give one example.