A tuning fork of frequency 200 Hz is in unison with a sonometer wire. The number of beats heard

step 1 In this question we will be understanding some basic concepts of the oscillation. The question i

A tuning fork of frequency 200 Hz is in unison with a...

A tuning fork of frequency $200 \mathrm{~Hz}$ is in unison with a sonometer wire. The number of beats heard per second when the tension is increased by $1 \%$ is $\ldots \ldots \ldots .$
(A) 1
(B) 2
(C) 4
(D) $0.5$

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Key Concepts

Beat Frequency

Beat frequency is the phenomenon of periodic amplitude fluctuations that occur when two sound waves of slightly different frequencies are superimposed. The beat frequency is equal to the absolute difference between the two frequencies, and it determines how many beats (or pulses) per second are heard. This concept is widely used in tuning musical instruments and in various applications of wave interference.

Fundamental Frequency of a Vibrating String

The fundamental frequency of a stretched string is determined by its length, tension, and linear mass density. It is given by the equation f = (1/(2L))?(T/?), showing that the frequency is directly proportional to the square root of the tension. This relationship is essential for understanding how changes in tension affect the pitch produced by the string.

Small Percentage Change Approximation

When a parameter in a formula is altered by a small percentage, its effect on a function can be approximated by using first order (linear) approximations. In cases where the function depends on the square root, as with the string's frequency and tension, a small increase in tension results in roughly half that percentage increase in frequency. This approximation technique is useful for quickly estimating the impact of minor changes in physical quantities.

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