Question

Standing waves are produced in $10\, m$ long stretched string. If the string vibrates in $5$ segments and wave velocity is $20\,m/s$, its frequency is

• A. 5 Hz
• B. 4 Hz
• C. 2 Hz
• D. 10 Hz

Answer 1

The Correct Option is A

To find the frequency of the standing waves on a stretched string, we can use the relationship between the length of the string, the number of segments (or loops), and the wave velocity. Here's how the calculation is done step-by-step:

1. The formula for the frequency $f$ when standing waves are formed can be expressed as:

   f = \frac{n \cdot v}{2L}

   where:

   • $n$ is the number of segments or loops,
   • $v$ is the wave velocity,
   • $L$ is the length of the string.

2. Given:

   • Length of the string L = 10\, m
   • Number of segments n = 5
   • Velocity of the wave v = 20\, m/s

3. Substitute the given values into the formula:

   f = \frac{5 \cdot 20}{2 \cdot 10}

   Calculate the frequency:

   f = \frac{100}{20} = 5\, Hz

4. Therefore, the frequency of the standing waves is 5\, Hz.

5. Conclusion: The correct answer is 5 Hz.