Question:
Two sources of sound placed close to each other are emitting progressive waves given by
\(y_{1}=4\,\sin (600\pi t)\) and \(y_{2}=5\,\sin (608\pi t)\).
An observer located near these two sources of sound will hear
Two sources of sound placed close to each other are emitting progressive waves given by
\(y_{1}=4\,\sin (600\pi t)\) and \(y_{2}=5\,\sin (608\pi t)\).
An observer located near these two sources of sound will hear
\(y_{1}=4\,\sin (600\pi t)\) and \(y_{2}=5\,\sin (608\pi t)\).
An observer located near these two sources of sound will hear
Show Hint
Beat frequency is the difference of the two frequencies, and the intensity ratio comes from the maximum and minimum amplitudes.
Updated On: Nov 12, 2026
- \(4\) beats/s with intensity ratio \(25:16\) between waxing and waning.
- \(8\) beats/s with intensity ratio \(25:16\) between waxing and waning.
- \(8\) beats/s with intensity ratio \(81:1\) between waxing and waning.
- \(4\) beats/s with intensity ratio \(81:1\) between waxing and waning.
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
For \(y=a\sin(\omega t)\), the frequency is \(f=\frac{\omega}{2\pi}\). Beats occur at the difference of the two frequencies.
Step 2: Calculation
\(f_{1}=\frac{600\pi}{2\pi}=300\ \text{Hz}\) and \(f_{2}=\frac{608\pi}{2\pi}=304\ \text{Hz}\), so the beat frequency is \(4\) beats/s. The maximum amplitude is \(4+5=9\) and the minimum is \(5-4=1\).
Step 3: Compare the options
Intensity is proportional to amplitude squared, so \(\frac{I_{max}}{I_{min}}=\frac{81}{1}\). So the answer is 4 beats/s with ratio \(81:1\).
Final Answer:
The observer hears 4 beats/s with an intensity ratio of \(81:1\). \[ \boxed{\text{(D) }\text{4 beats/s with intensity ratio 81:1 between waxing and waning}} \]
For \(y=a\sin(\omega t)\), the frequency is \(f=\frac{\omega}{2\pi}\). Beats occur at the difference of the two frequencies.
Step 2: Calculation
\(f_{1}=\frac{600\pi}{2\pi}=300\ \text{Hz}\) and \(f_{2}=\frac{608\pi}{2\pi}=304\ \text{Hz}\), so the beat frequency is \(4\) beats/s. The maximum amplitude is \(4+5=9\) and the minimum is \(5-4=1\).
Step 3: Compare the options
Intensity is proportional to amplitude squared, so \(\frac{I_{max}}{I_{min}}=\frac{81}{1}\). So the answer is 4 beats/s with ratio \(81:1\).
Final Answer:
The observer hears 4 beats/s with an intensity ratio of \(81:1\). \[ \boxed{\text{(D) }\text{4 beats/s with intensity ratio 81:1 between waxing and waning}} \]
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