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A string has a length of 5 cm between fi...

A string has a length of 5 cm between fixed points and has a fundamental frequency of 20 Hz. What is the frequency of the second overtone?

A

40 Hz

B

50 Hz

C

60 Hz

D

30 Hz

Text Solution

AI Generated Solution

The correct Answer is:
To find the frequency of the second overtone of a string fixed at both ends, we can follow these steps: ### Step 1: Understand the Fundamental Frequency The fundamental frequency (first harmonic) of a string fixed at both ends is given as \( f_1 = 20 \, \text{Hz} \). ### Step 2: Identify the Harmonics For a string fixed at both ends: - The first harmonic (fundamental frequency) corresponds to \( n = 1 \) and has a frequency of \( f_1 = n \cdot f \). - The second harmonic (first overtone) corresponds to \( n = 2 \) and has a frequency of \( f_2 = 2 \cdot f_1 \). - The third harmonic (second overtone) corresponds to \( n = 3 \) and has a frequency of \( f_3 = 3 \cdot f_1 \). ### Step 3: Calculate the Frequency of the Second Overtone Since the second overtone corresponds to the third harmonic: \[ f_3 = 3 \cdot f_1 \] Substituting the value of \( f_1 \): \[ f_3 = 3 \cdot 20 \, \text{Hz} = 60 \, \text{Hz} \] ### Final Answer The frequency of the second overtone is \( 60 \, \text{Hz} \). ---
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