Question

Two tuning forks of frequencies 320 Hz and 323 Hz are vibrated together. The time interval between a maximum sound and its adjacent minimum sound heard by an observer is

• A. 1/6 s
• B. 1/3 s
• C. 1/12 s
• D. 1/9 s

Hint:

The beat frequency is the number of maxima per second ($f_{beat} = |f_1 - f_2|$). The time between two consecutive maxima is the beat period, $T_{beat} = 1/f_{beat}$. The time between a maximum and the next minimum is half the beat period, $T_{beat}/2$.

Answer 1

The Correct Option is A

When two sound waves of slightly different frequencies interfere, they produce a phenomenon called beats.
The beat frequency ($f_{beat}$) is the difference between the two frequencies.
$f_1 = 320$ Hz.
$f_2 = 323$ Hz.
$f_{beat} = |f_2 - f_1| = |323 - 320| = 3$ Hz.
The beat frequency represents the number of times the sound intensity becomes maximum per second. So, there are 3 maxima (or "beats") per second.
The time interval between two consecutive maxima is the beat period, $T_{beat}$.
$T_{beat} = \frac{1}{f_{beat}} = \frac{1}{3}$ s.
The sound intensity varies sinusoidally between maximum and minimum. A full cycle consists of a maximum followed by a minimum, then another maximum.
The time interval between a maximum and the very next (adjacent) minimum is half of the beat period.
Time interval = $\frac{T_{beat}}{2} = \frac{1/3 \text{ s}}{2} = \frac{1}{6}$ s.