Question

One of the harmonic frequencies for a particular string under tension is 325 Hz.The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?

Short answer

The harmonic frequency that is next higher after the harmonic frequency 195 Hz is 260 Hz.

Step-by-step solution

Given data

Under the tension one of the harmonic frequency for a particular string is$f_1=325\mathrm{Hz}$ and next higher frequency is$f_2=390\mathrm{Hz}$

One of the lower harmonic frequencies is$f{\text{'}}_1=195\mathrm{Hz}$

Understanding the concept of resonant frequency

The harmonic frequencies are integer multiples of the lowest harmonic frequency. Therefore, the difference between two successive frequencies is the fundamental frequency. Adding the fundamental frequency to the given frequency, we can find the successive higher frequency after it.

Calculation for the harmonic frequency

The resonant frequency of the string is given as:

$f\text{'}=nf$

Where, n = 1,2,3 and f is the fundamental frequency.

Hence, the fundamental frequency is 390 - 325 = 65 Hz

The frequency next higher after the given frequency = the given frequency + the fundamental frequency

Therefore, the frequency next higher after the harmonic frequency 195 Hz is

195+65=260 Hz

Hence, the harmonic frequency next higher after the harmonic frequency 195 Hz is 260 Hz.