Question

Given are two tuning forks near one another, one of them is of unknown frequency and the other is of frequency $591\text{Hz}$. We can hear beats of maximal intensity $I_0,5$ times each second. Then -

• A. Unknown frequency may be $596\text{Hz}$
• B. Unknown frequency may be $586\text{Hz}$
• C. Difference in frequency of two tuning forks is $5\text{Hz}$
• D. Intensity at time t = $\frac{27}{20}\text{sec is}\frac{I_0}{2}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Unknown frequency may be $596\text{Hz}$
B Unknown frequency may be $586\text{Hz}$
C Difference in frequency of two tuning forks is $5\text{Hz}$
D Intensity at time t = $\frac{27}{20}\text{sec is}\frac{I_0}{2}$

Beat frequency : $f_1-f_2=\pm 5$
$\Rightarrow f_1=f_2\pm 5$
$f_1=f_2+5\text{or}{f}_1=f_2-5$
$f_1=596\text{or}{f}_1=586\text{Hz}$
Intensity : $I=I_{0}co{s}^2\left(\frac{{\omega }_{1}t-{\omega }_{2}t}{2}\right)$
where $f$ = frequency
$I$ = intensity
$I_0$ = maximum intensity
$=I_{0}co{s}^2\frac{2\pi }{2}(f_1-f_2)t$
$=I_{0}co{s}^2(\pi \times 5\times \frac{27}{20})$
$=I_{0}co{s}^2\frac{3\pi }{4}=\frac{I_0}{2}$