If the amplitude of sound is doubled and the frequency...

If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be
(a) increased by a factor of 2
(b) decreased by a factor of 2
(c) decreased by a factor of 4
(d) unchanged

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Key Concepts

Sound Intensity

Sound intensity is the measure of energy transmitted by a sound wave per unit area per unit time. It typically depends on the square of the wave’s amplitude and, when derived from the expression involving particle velocity, also on the square of the angular frequency, reflecting how both the strength of the wave and its oscillatory rate contribute to the energy flow.

Amplitude

Amplitude refers to the maximum displacement from equilibrium in a wave and is directly related to the pressure variations in a sound wave. Since sound intensity is proportional to the square of the amplitude, any change in amplitude (such as doubling) results in a fourfold change in that component of intensity.

Frequency and Angular Frequency

Frequency, the number of oscillations per second, directly impacts the energy of a sound wave via its angular frequency (? = 2?f). In expressions for intensity that involve angular frequency, the intensity is proportional to ?². Thus, reducing the frequency (and therefore ?) significantly decreases the intensity, as demonstrated by a one?fourth decrease in frequency yielding a factor of (1/4)² reduction from the frequency component.

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