When two waves of almost equal frequencies `v_(1)` and `v_(2)` reach at a point simultaneously, the time interval between successive maxima is

Options

A. `upsilon_(1)+upsilon_(2)`
B. `upsilon_(1)-upsilon_(2)`
C. `1/(upsilon_(1)+upsilon_(2))`
D. `1/(upsilon_(1)-upsilon_(2))`

Explanation

To solve the problem of finding the time interval between successive maxima when two waves of almost equal frequencies \( v_1 \) and \( v_2 \) reach a point simultaneously, we can follow these steps:

### Step 1: Understand the Concept of Beat Frequency
When two waves of slightly different frequencies interfere, they create a phenomenon known as "beats." The beat frequency \( f_b \) is given by the absolute difference between the two frequencies:
\[ f_b = |v_1 - v_2| \]

### Step 2: Relate Frequency to Time
The time period \( T \) of a wave is the reciprocal of its frequency. Therefore, the time interval between successive maxima (or minima) can be expressed in terms of the beat frequency:
\[ T_b = \frac{1}{f_b} \]

### Step 3: Substitute the Beat Frequency
Substituting the expression for beat frequency into the equation for time interval gives:
\[ T_b = \frac{1}{|v_1 - v_2|} \]

### Conclusion
Thus, the time interval between successive maxima when two waves of almost equal frequencies \( v_1 \) and \( v_2 \) reach a point simultaneously is:
\[ T_b = \frac{1}{|v_1 - v_2|} \]

### Final Answer
The time interval between successive maxima is \( \frac{1}{|v_1 - v_2|} \).

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