Two identical flutes produce fundamental notes of frequency 300 Hz at $27^\circ$ C. If the temperature of air in one flute is increased to $31^\circ$ C, the number of the beats heard per second will be
Text Solution
Verified by ExpertsB
Velocity of sound increases if the temperature increases.
So with $v = n \lambda$ , if V increases n will increase
at $27^\circ C,v_1=n\lambda$ , at $31^\circ \mathrm{C}, v_2 = (n + x) \lambda$
Now using $v \propto \sqrt{T}$ $\therefore v = \sqrt{\frac{\gamma RT}{M}}$
$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}} = \frac{n+x}{n}$
⇒ ⇒ $\frac{300+x}{300} = \sqrt{\frac{(273+31)}{(273+27)}} = \sqrt{\frac{304}{300}} = \sqrt{\frac{300+4}{300}}$
⇒ ⇒ $1 + \frac{x}{300} = \left(1 + \frac{4}{300}\right)^{\frac{1}{2}} = \left(1 + \frac{1}{2} \times \frac{4}{300}\right)$
⇒ ⇒ x = 2.
$[\therefore (1+x)^n = 1 + nx]$
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems