Question:
A car is approaching a factory siren that has a frequency of 510 Hz. The speed of sound in air is 340 m/s. If the apparent frequency of the sound as heard by the car driver is 600 Hz, then the speed of the car is:
A car is approaching a factory siren that has a frequency of 510 Hz. The speed of sound in air is 340 m/s. If the apparent frequency of the sound as heard by the car driver is 600 Hz, then the speed of the car is:
Show Hint
For Doppler effect with moving observer and stationary source: \(f' = f (v + v_o)/v\). Solve for \(v_o\) when apparent frequency is given.
Updated On: Jun 19, 2026
- 60 m/s
- 33.3 m/s
- 50.5 m/s
- 80 m/s
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Use Doppler effect formula.
\[ f' = f \frac{v + v_o}{v} \quad \text{(source stationary, observer moving towards source)} \] where \(v = 340~\text{m/s}\), \(f = 510~\text{Hz}\), \(f' = 600~\text{Hz}\).
Step 2: Solve for observer speed \(v_o\).
\[ 600 = 510 \frac{340 + v_o}{340} \Rightarrow \frac{600}{510} = \frac{340 + v_o}{340} \] \[ \frac{600}{510} \cdot 340 = 340 + v_o \Rightarrow 400 = 340 + v_o \Rightarrow v_o = 60~\text{m/s} \]
Step 3: Conclusion.
The car is moving at 60 m/s towards the siren.
\[ f' = f \frac{v + v_o}{v} \quad \text{(source stationary, observer moving towards source)} \] where \(v = 340~\text{m/s}\), \(f = 510~\text{Hz}\), \(f' = 600~\text{Hz}\).
Step 2: Solve for observer speed \(v_o\).
\[ 600 = 510 \frac{340 + v_o}{340} \Rightarrow \frac{600}{510} = \frac{340 + v_o}{340} \] \[ \frac{600}{510} \cdot 340 = 340 + v_o \Rightarrow 400 = 340 + v_o \Rightarrow v_o = 60~\text{m/s} \]
Step 3: Conclusion.
The car is moving at 60 m/s towards the siren.
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET doppler effect Questions
- When both the source of sound and observer approach each other with a speed equal to 10% of the speed of sound, then the percentage change in frequency heard by the observer is nearly
- The apparent frequency of a siren increases as the source approaches a stationary observer. This phenomenon is known as
- Two cars are moving towards each other at the speed of \(50\,\text{m s}^{-1}\). If one of the cars blows a horn at a frequency of \(250\,\text{Hz}\), the wavelength of the sound perceived by the driver of the other car is
\[ \text{(Speed of sound in air }=350\,\text{m s}^{-1}\text{)} \]
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions