Question

Two identical straight wires are stretched so as to produce 6 beats/s when vibrating simultaneously. On changing the tension slightly in one of them, the beat frequency remains unchanged. Denoting by $T_1,T_2$ the higher and the lower initial tension in the strings, then it could be said that while making the above changes in tension

• A. $T_2$ was decreased
• B. $T_2$ was increased
• C. $T_1$ was decreased
• D. $T_1$ was increased

Answer 1

Answer: (C)

$T_1$ was decreased

Answer 2

\hspace35mm T_1 >T_2
\therefore\hspace25mm v_1 >v_2
or \hspace25mm f_1 > f_2
and \hspace20mm f_1 - f_2=6\, Hz
Now, if $T_1$ is increased, $f_1$ will increase or $f_1 - f_2$ will
increase. Therefore, (d) option is wrong.
If $T_1$ is decreased, $f_1$ will decrease and it may be possible that
now $f_2-f_1$ become 6 Hz.Therefore, (c) option is correct.

Similarly, when $T_2$ is increased, $f_2$ will increase and again
$f_2-f_1$ may become equal to 6 Hz. So, (b) is also correct.
But (a) is wrong.