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Physics Chapter 9 : Topic 1
Wave Intensity and Amplitude
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The intensity of a wave is defined as:
Reasoning: Intensity is the rate of energy transfer (power) through a unit area:$\mathbf{I =}$ $\frac{\mathbf{P}}{\mathbf{A}}$
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The SI unit of intensity is:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}\mathbf{=}\frac{\mathbf{Power\ }\left( \mathbf{W} \right)}{\mathbf{Area\ }\left( \mathbf{m}^{\mathbf{2}} \right)}\mathbf{=}\mathbf{Wm}^{\mathbf{- 2}}$
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A wave carries $\mathbf{120\ W}$ of power through an area of $\mathbf{6\ m}^{\mathbf{2}}$. Its intensity is:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}\mathbf{=}\frac{\mathbf{120}}{\mathbf{6}}\mathbf{= 20\ }\mathbf{Wm}^{\mathbf{- 2}}$
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Intensity measures:
Reasoning: Intensity describes the rate of energy transfer through unit area.
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If the transmitted power doubles while area remains constant, intensity becomes:
Reasoning: Intensity is directly proportional to power.
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If the area through which a wave spreads doubles while power remains constant, intensity:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}$ ; Increasing area decreases intensity.
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Two waves carry the same power. The wave spread over the smaller area has:
Reasoning: Smaller area means more power per unit area.
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Which quantity directly affects intensity?
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}$ ; depends on both quantities.
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A wave of intensity $\mathbf{50\ }\mathbf{W\ m}^{\mathbf{- 2}}$ passes through an area of $\mathbf{4\ m}^{\mathbf{2}}$. The power transmitted is:
Reasoning: $\mathbf{P}\mathbf{=}\mathbf{IA}\mathbf{= (50)(4) = 200\ W}$
10 / 30
A wave carries $\mathbf{300\ W}$ through an area of $\mathbf{15\ m}^{\mathbf{2}}$. Its intensity is:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}\mathbf{=}\frac{\mathbf{300}}{\mathbf{15}}\mathbf{= 20\ }\mathbf{Wm}^{\mathbf{- 2}}$
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For a progressive wave, intensity is proportional to:
Reasoning: $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$
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If the amplitude of a wave doubles, its intensity becomes:
Reasoning: $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{(2A)}^{\mathbf{2}}\mathbf{\propto 4}\mathbf{A}^{\mathbf{2}}$
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If amplitude becomes three times larger, intensity becomes:
Reasoning: $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{(3A)}^{\mathbf{2}}\mathbf{\propto 9}\mathbf{A}^{\mathbf{2}}$
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If amplitude is reduced to half, intensity becomes:
Reasoning: $\left( \frac{\mathbf{A}}{\mathbf{2}} \right)^{\mathbf{2}}\mathbf{=}\frac{\mathbf{A}^{\mathbf{2}}}{\mathbf{4}}$
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When intensity increases by a factor of $\mathbf{16}$, amplitude increases by a factor of:
Reasoning: $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{A =}\sqrt{\mathbf{16}}\mathbf{= 4}$
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The amplitude ratio of two waves is $\mathbf{2\ :1}$. Their intensity ratio is:
Reasoning: $\mathbf{I}_{\mathbf{1}}\mathbf{\ :}\mathbf{I}_{\mathbf{2}}\mathbf{=}\mathbf{(2)}^{\mathbf{2}}\mathbf{\ :}\mathbf{(1)}^{\mathbf{2}}\mathbf{= 4\ :1}$
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A wave has intensity $\mathbf{100\ }\mathbf{W\ m}^{\mathbf{- 2}}$. If its amplitude doubles, the new intensity is:
Reasoning: $\mathbf{I}_{\mathbf{2}}\mathbf{=}{\mathbf{4\ }\mathbf{I}}_{\mathbf{1}}\mathbf{= 400\ }\mathbf{Wm}^{\mathbf{- 2}}$
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If intensity becomes $\mathbf{9}$ times larger, the amplitude becomes:
Reasoning: $\mathbf{I \propto}\mathbf{A}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{A =}\sqrt{\mathbf{9}}\mathbf{= 3}$
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Two waves have amplitudes $\mathbf{4\ cm}$ and $\mathbf{2\ cm}$. The intensity ratio is:
Reasoning: $\mathbf{I}_{\mathbf{1}}\mathbf{\ :}\mathbf{I}_{\mathbf{2}}\mathbf{=}\mathbf{4}^{\mathbf{2}}\mathbf{\ :}\mathbf{2}^{\mathbf{2}}\mathbf{= 16\ :4 = 4\ :1}$
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If intensity decreases to one-ninth of its original value, amplitude becomes:
Reasoning: $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$ $\mathbf{\Longrightarrow}$ $\mathbf{A}$ $\mathbf{=}$ $\sqrt{\frac{\mathbf{1}}{\mathbf{9}}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{3}}$
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A source emits constant power. If the area over which energy spreads becomes four times larger, intensity becomes:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{P}}{\mathbf{A}}$
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Which change causes the greatest increase in intensity?
Reasoning: Doubling amplitude increases intensity fourfold, greater than doubling power.
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If power becomes four times larger and area becomes twice as large, intensity becomes:
Reasoning: $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{4P}}{\mathbf{2A}}\mathbf{= 2}\mathbf{I}$
24 / 30
A wave passes through $\mathbf{8\ m}^{\mathbf{2}}$ with intensity $\mathbf{25\ }\mathbf{W\ m}^{\mathbf{- 2}}$. Power transmitted is:
Reasoning: $\mathbf{P = IA}\mathbf{= (25)(8) = 200\ W}$
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The intensity of a wave depends most strongly on:
Reasoning: Since intensity varies with the square of amplitude, small amplitude changes cause large intensity changes.
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Which statement is correct?
Reasoning: For progressive waves $\mathbf{\Longrightarrow}$ $\mathbf{I}\mathbf{\propto}\mathbf{A}^{\mathbf{2}}$
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A wave’s amplitude increases by $\mathbf{50\%}$. The new intensity is:
Reasoning: $\mathbf{I}_{\mathbf{2}}\mathbf{=}\mathbf{(1.5)}^{\mathbf{2}}\mathbf{\ }\mathbf{I}_{\mathbf{1}}\mathbf{= 2.}\mathbf{25\ }\mathbf{I}_{\mathbf{1}}$
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If intensity becomes $\mathbf{25}$ times larger, amplitude becomes:
Reasoning: $\mathbf{A =}\sqrt{\mathbf{25}}\mathbf{= 5}$
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Two waves have intensity ratio $\mathbf{16\ :1}$. Their amplitude ratio is:
Reasoning: $\mathbf{A}_{\mathbf{1}}\mathbf{\ :}\mathbf{A}_{\mathbf{2}}\mathbf{=}\sqrt{\mathbf{16}}\mathbf{\ :1 = 4\ :1}$
30 / 30
A wave source produces four times the amplitude and spreads over twice the area while power is proportional to ${\mathbf{(}\mathbf{amplitude}\mathbf{)}}^{\mathbf{2}}$. The intensity compared to the original becomes:
Reasoning: Amplitude $\mathbf{\times 4}$ $\mathbf{\Longrightarrow}$ Power $\mathbf{\times 16}$ $\mathbf{\Longrightarrow}$ Area $\mathbf{\times 2}$ $\mathbf{\Longrightarrow}$ $\mathbf{I}\mathbf{=}$ $\frac{\mathbf{16P}}{\mathbf{2A}}\mathbf{=}\mathbf{8}\mathbf{I}$
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