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Q. 37

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?

The length of the string is 5.40 m

See the step by step solution

Step by Step Solution

Step 1: Write the given information 

Third-harmonic frequency, n= 3The amplitude of the wave at x=30cm is Amax/2

Step 2: To determine the length of the string

The general expression of the amplitude of the wave at any distance x

According to the question Since it is three harmonic vibrations, there would be three loops with the length λ/2. Therefore, the total length of the string is given by Thus the length of the string is 5.40 m

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