Search any question & find its solution
Question:
Answered & Verified by Expert
A whistle of frequency $660 \mathrm{~Hz}$ moves in a circle of radius $1 \mathrm{~m}$ at an angular speed of $10 \mathrm{rad} / \mathrm{s}$. The highest frequency heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound $=340 \mathrm{~m} / \mathrm{s}$.)
Options:
Solution:
1864 Upvotes
Verified Answer
The correct answer is:
$680 \mathrm{~Hz}$
Given, frequency whistle $f_0=660 \mathrm{~Hz}$, speed of
sound $=340 \mathrm{~m} / \mathrm{s}$
angular speed of whistle, $\omega=10 \mathrm{rad} / \mathrm{s}$ and radius of circle, $r=1 \mathrm{~m}$.
Since, we know that the maximum frequency heard by listener, if whistle has tangential velocity towards the listener as shown in figure,
linear velocity, $v=\omega r$
$=10 \times 1=10 \mathrm{~m} / \mathrm{s}$
As, given that, there is long distance between whistle and listener i.e., $\theta \approx 0$.
Now, the apparent frequency,
$\begin{aligned} & f=\frac{f_0 v}{v-v_s} \\ & f=\frac{660 \times 340}{340-10}=680 \mathrm{~Hz}\end{aligned}$
Hence, the correct option is (d).
sound $=340 \mathrm{~m} / \mathrm{s}$
angular speed of whistle, $\omega=10 \mathrm{rad} / \mathrm{s}$ and radius of circle, $r=1 \mathrm{~m}$.
Since, we know that the maximum frequency heard by listener, if whistle has tangential velocity towards the listener as shown in figure,
linear velocity, $v=\omega r$
$=10 \times 1=10 \mathrm{~m} / \mathrm{s}$
As, given that, there is long distance between whistle and listener i.e., $\theta \approx 0$.
Now, the apparent frequency,
$\begin{aligned} & f=\frac{f_0 v}{v-v_s} \\ & f=\frac{660 \times 340}{340-10}=680 \mathrm{~Hz}\end{aligned}$
Hence, the correct option is (d).
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.