Answer
Verified
35.4k+ views
Hint: Use the Doppler Effect concept. Note the direction in which the source is moving and find the ratio of frequency by the condition. Now, substitute the value in terms of frequency of source and simplify to find the value of \[\;{v_s}\].
Complete step-by-step solution:
Whenever there is a relative motion between a source and the observer, the frequency of sound heard by the observer is different from the actual frequency of sound emitted by the source. The frequency observed by the observer is called apparent frequency. It can be more or lesser than the actual frequency which depends on the relative motion.
In this case the source is moving towards the observer, so apparent frequency =
$n' = n\left( {\dfrac{v}{{v - {v_s}}}} \right)$
Where,
n=frequency of source
v=velocity of sound
\[\;{v_s}\] = velocity of source
According to the problem,
$
n' = n + \dfrac{{50}}{{100}}n \\
n' = \dfrac{3}{2}n \\
$
Substituting the value in the expression, we get
$
\dfrac{3}{2}n = n\left( {\dfrac{v}{{v - {v_s}}}} \right) \\
3v - 3{v_s} = 2v \\
{v_s} = \dfrac{v}{3} \\
{v_s} = \dfrac{{330}}{3} \\
{v_s} = 110m{s^{ - 1}} \\
$
So, to increase the apparent frequency by 50% the velocity of source should be 110m/s.
A is the correct option.
Note: Some conventions:
1. The direction of v is always taken from source to observer
2. All the velocities in the direction of v are taken positive
3. All the velocities in the opposite direction of v are taken negative.
Complete step-by-step solution:
Whenever there is a relative motion between a source and the observer, the frequency of sound heard by the observer is different from the actual frequency of sound emitted by the source. The frequency observed by the observer is called apparent frequency. It can be more or lesser than the actual frequency which depends on the relative motion.
In this case the source is moving towards the observer, so apparent frequency =
$n' = n\left( {\dfrac{v}{{v - {v_s}}}} \right)$
Where,
n=frequency of source
v=velocity of sound
\[\;{v_s}\] = velocity of source
According to the problem,
$
n' = n + \dfrac{{50}}{{100}}n \\
n' = \dfrac{3}{2}n \\
$
Substituting the value in the expression, we get
$
\dfrac{3}{2}n = n\left( {\dfrac{v}{{v - {v_s}}}} \right) \\
3v - 3{v_s} = 2v \\
{v_s} = \dfrac{v}{3} \\
{v_s} = \dfrac{{330}}{3} \\
{v_s} = 110m{s^{ - 1}} \\
$
So, to increase the apparent frequency by 50% the velocity of source should be 110m/s.
A is the correct option.
Note: Some conventions:
1. The direction of v is always taken from source to observer
2. All the velocities in the direction of v are taken positive
3. All the velocities in the opposite direction of v are taken negative.
Recently Updated Pages
To get a maximum current in an external resistance class 1 physics JEE_Main
f a body travels with constant acceleration which of class 1 physics JEE_Main
A hollow sphere of mass M and radius R is rotating class 1 physics JEE_Main
If the beams of electrons and protons move parallel class 1 physics JEE_Main
Two radioactive nuclei P and Q in a given sample decay class 1 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Other Pages
Oxidation state of S in H2S2O8 is A 6 B 7 C +8 D 0 class 12 chemistry JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
Dissolving 120g of urea molwt60 in 1000g of water gave class 11 chemistry JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main