Sound and Resonance

Objective: Interpret reflected sound and changing observed frequency.

An echo is reflected sound heard after a delay. If an acoustic pulse travels to a reflector and back in time t at speed v, one-way distance is d = vt/2, because the sound traverses the path twice. A 0.4 s round trip at 340 m/s gives a reflector distance of 68 m. The Doppler effect changes observed frequency when source and observer move relative to each other: approach generally raises observed frequency and recession lowers it in the common stationary-medium sound model. The source’s emitted frequency need not change. Echo strength and timing depend on surfaces and environment; Doppler reasoning should identify which objects move and the medium frame.

Objective: Apply sound and resonance to calculations, evidence, and specified situations.

Sound is a mechanical wave requiring a medium. Pitch is related to frequency, while loudness depends on intensity and perception. An echo travels to the reflector and back, so distance is vt/2. Approaching motion raises observed frequency in the ordinary subsonic Doppler setting; receding motion lowers it. Sound speed depends on the medium and temperature; the exercises explicitly assume 340 m/s. Do not apply that value to all materials or use light-wave behavior as a direct substitute. Resonance is a strong driven response near a natural frequency, limited by damping. For an ideal string fixed at both ends, the fundamental has wavelength 2L and frequency v/(2L).