Question:
Two simple harmonic sound waves travelling in the same direction are given by \(y_{1}(x,t)=A\sin (0.5\pi x-100\pi t)\) and \(y_{2}(x,t)=A\sin (0.46\pi x-92\pi t)\)
The number of times, a stationary listener can hear sound of maximum intensity in one second is
Two simple harmonic sound waves travelling in the same direction are given by \(y_{1}(x,t)=A\sin (0.5\pi x-100\pi t)\) and \(y_{2}(x,t)=A\sin (0.46\pi x-92\pi t)\)
The number of times, a stationary listener can hear sound of maximum intensity in one second is
The number of times, a stationary listener can hear sound of maximum intensity in one second is
Show Hint
Read the frequencies from the coefficient of t. The number of maxima per second is the beat frequency.
Updated On: Nov 12, 2026
- \(3\)
- \(4\)
- \(6\)
- \(8\)
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
Two waves of slightly different frequencies produce beats. The listener hears a maximum once per beat period.
Step 2: Find the Frequencies
From \(\omega=2\pi f\): \(f_1=\dfrac{100\pi}{2\pi}=50\text{ Hz}\) and \(f_2=\dfrac{92\pi}{2\pi}=46\text{ Hz}\).
Step 3: Calculation
Beat frequency \(=f_1-f_2=50-46=4\text{ Hz}\).
Step 4: Compare the options
So 4 maxima are heard per second, the second option.
Final Answer:
A listener hears the maximum intensity 4 times in a second. \[ \boxed{\text{(B) }4} \]
Two waves of slightly different frequencies produce beats. The listener hears a maximum once per beat period.
Step 2: Find the Frequencies
From \(\omega=2\pi f\): \(f_1=\dfrac{100\pi}{2\pi}=50\text{ Hz}\) and \(f_2=\dfrac{92\pi}{2\pi}=46\text{ Hz}\).
Step 3: Calculation
Beat frequency \(=f_1-f_2=50-46=4\text{ Hz}\).
Step 4: Compare the options
So 4 maxima are heard per second, the second option.
Final Answer:
A listener hears the maximum intensity 4 times in a second. \[ \boxed{\text{(B) }4} \]
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