Question

select the higher harmonics of a string fixed at both ends that has a fundamental frequency of 80 hz
120 hz
200 hz
80 hz
240 hz
160 hz

Explanation:

Step1: Recall the formula for harmonics

For a string fixed at both ends, the \(n^{th}\) harmonic frequency \(f_n = n\times f_1\), where \(f_1\) is the fundamental frequency and \(n = 1,2,3,\cdots\)

Step2: Check each option

• For \(f = 120\space Hz\): If \(f_n=120\space Hz\) and \(f_1 = 80\space Hz\), then \(n=\frac{f_n}{f_1}=\frac{120}{80}=1.5\). Since \(n\) is not an integer, \(120\space Hz\) is not a harmonic.
• For \(f = 200\space Hz\): \(n=\frac{200}{80}=2.5\). Since \(n\) is not an integer, \(200\space Hz\) is not a harmonic.
• For \(f = 80\space Hz\): \(n = 1\). This is the fundamental frequency, not a higher - harmonic.
• For \(f = 240\space Hz\): \(n=\frac{240}{80}=3\). Since \(n = 3\) (an integer), \(240\space Hz\) is a harmonic (\(3^{rd}\) harmonic).
• For \(f = 160\space Hz\): \(n=\frac{160}{80}=2\). Since \(n = 2\) (an integer), \(160\space Hz\) is a harmonic (\(2^{nd}\) harmonic).

Answer:

\(160\space Hz\), \(240\space Hz\)