When two tuning forks (fork 1 and fork 2 ) are sounded...

Name: Problem 291, Chapter 9: A Complete Resource Book in Physics for JEE Main
Uploaded: 2022-01-26T13:01:18-08:00
Duration: 3 min 33 s
Channel: Mahammadabrar Liyakatbhai Mamon
Description: When two tuning forks (fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2 ? (A) 202 Hz (B) 200 Hz (C) 204 Hz (D) 196 Hz

When two tuning forks (fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is $200 \mathrm{~Hz}$, then what was the original frequency of fork $2 ? (A) $202 \mathrm{~Hz}$ (B) $200 \mathrm{~Hz}$ (C) $204 \mathrm{~Hz}$ (D) $196 \mathrm{~Hz}$

When two tuning forks (fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is $200 \mathrm{~Hz}$, then what was the original frequency of fork $2 ?
(A) $202 \mathrm{~Hz}$
(B) $200 \mathrm{~Hz}$
(C) $204 \mathrm{~Hz}$
(D) $196 \mathrm{~Hz}$

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Key Concepts

Frequency Difference Analysis

Analyzing the difference in frequencies between two sound sources using beat frequencies provides a method to infer unknown frequencies. By comparing the observed beat frequency before and after a known modification, one can deduce the change in frequency and the original frequency of the source.

Effect of Mass on Frequency

The frequency of a tuning fork (or any oscillatory system) is influenced by its mass and stiffness. Adding mass, such as attaching tape, increases the inertia of the fork and consequently lowers its natural frequency. This concept is crucial in understanding how modifications to a system adjust its oscillatory behavior.

Beat Frequency

Beat frequency is the phenomenon that occurs when two waves of nearly the same frequency interfere, causing resultant amplitude variations at a frequency equal to the absolute difference between the two original frequencies. This principle allows one to determine the difference between frequencies when direct measurement is difficult.

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