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For a certain stretched string, three co...

For a certain stretched string, three consecutive resonance frequencies are observed as 105, 175 and 245 Hz respectively. Then, the fundamental frequency is

A

30 Hz

B

45 Hz

C

35 Hz

D

None of these

Text Solution

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The correct Answer is:
To find the fundamental frequency of a stretched string given its resonance frequencies, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Frequencies**: The three consecutive resonance frequencies are 105 Hz, 175 Hz, and 245 Hz. 2. **Find the Greatest Common Divisor (GCD)**: The fundamental frequency of the string can be determined by finding the GCD of the given frequencies. The GCD will give us the fundamental frequency. 3. **Calculate GCD**: - First, we can list the factors of each frequency: - Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105 - Factors of 175: 1, 5, 7, 25, 35, 175 - Factors of 245: 1, 5, 7, 35, 49, 245 - The common factors among these three frequencies are 1, 5, 7, and 35. The greatest of these is 35. 4. **Conclusion**: Therefore, the fundamental frequency of the string is 35 Hz. ### Final Answer: The fundamental frequency is **35 Hz**. ---
To find the fundamental frequency of a stretched string given its resonance frequencies, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Given Frequencies**: The three consecutive resonance frequencies are 105 Hz, 175 Hz, and 245 Hz. 2. **Find the Greatest Common Divisor (GCD)**: The fundamental frequency of the string can be determined by finding the GCD of the given frequencies. The GCD will give us the fundamental frequency. ...
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