The frequency of the fourth harmonic (n = 4) of a vibrating string is 844 Hz. What is the fundamental frequency of the string? 844 Hz 106 Hz 422 Hz 211 Hz
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![### Harmonic Frequency Calculation
**Question:**
The frequency of the fourth harmonic (n = 4) of a vibrating string is 844 Hz. What is the fundamental frequency of the string?
**Options:**
- ⃝ 844 Hz
- ⃝ 106 Hz
- ⃝ 422 Hz
- ⃝ 211 Hz
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**Explanation:**
In physics, the frequency of the harmonics of a vibrating string can be determined using the relation:
\[ f_n = n \times f_1 \]
Where:
- \( f_n \) is the frequency of the n-th harmonic.
- \( n \) is the harmonic number.
- \( f_1 \) is the fundamental frequency.
Given:
- The frequency of the fourth harmonic \( f_4 \) is 844 Hz.
- The harmonic number \( n \) is 4.
We need to find the fundamental frequency, \( f_1 \).
Using the relation for the fourth harmonic:
\[ f_4 = 4 \times f_1 \]
Substituting the given value:
\[ 844 = 4 \times f_1 \]
Solving for \( f_1 \):
\[ f_1 = \frac{844}{4} \]
\[ f_1 = 211 \, \text{Hz} \]
Therefore, the fundamental frequency of the string is **211 Hz**.
Correct Option:
- ⃝ 211 Hz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fc0f41c-1d8b-41a4-aee9-3a82e03a5afd%2Fd74dd4fb-3ea2-43db-9316-e474f7bd7e54%2F9sjcku.png&w=3840&q=75)
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