Question:
Two stationary sources P and Q produce sounds of equal frequency of \(170\,Hz\). The velocity with which an observer has to move from source P towards source Q such that 8 beats are heard per second by the observer is:
Two stationary sources P and Q produce sounds of equal frequency of \(170\,Hz\). The velocity with which an observer has to move from source P towards source Q such that 8 beats are heard per second by the observer is:
Show Hint
For two equal-frequency sources and a moving observer:
\[
f_b=\frac{2fu}{v}.
\]
This shortcut is very useful in Doppler beat problems.
Updated On: Jun 18, 2026
- \(20\,ms^{-1}\)
- \(16\,ms^{-1}\)
- \(4\,ms^{-1}\)
- \(8\,ms^{-1}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
For a moving observer:
\[
f'=f\left(\frac{v\pm u}{v}\right).
\]
Moving towards one source increases frequency and moving away from the other decreases frequency.
Beat frequency is
\[
f_b=|f_1-f_2|.
\]
Step 1: Observed frequencies.
Towards source Q: \[ f_Q=f\left(\frac{v+u}{v}\right). \] Away from source P: \[ f_P=f\left(\frac{v-u}{v}\right). \]
Step 2: Calculate beat frequency.
\[ f_b = f_Q-f_P. \] \[ = f\left(\frac{v+u}{v}\right) - f\left(\frac{v-u}{v}\right). \] \[ = \frac{2fu}{v}. \]
Step 3: Use given values.
\[ 8 = \frac{2(170)u}{340}. \] \[ 8=u. \] \[ u=8\,ms^{-1}. \] Therefore \[ \boxed{8\,ms^{-1}}. \]
Step 1: Observed frequencies.
Towards source Q: \[ f_Q=f\left(\frac{v+u}{v}\right). \] Away from source P: \[ f_P=f\left(\frac{v-u}{v}\right). \]
Step 2: Calculate beat frequency.
\[ f_b = f_Q-f_P. \] \[ = f\left(\frac{v+u}{v}\right) - f\left(\frac{v-u}{v}\right). \] \[ = \frac{2fu}{v}. \]
Step 3: Use given values.
\[ 8 = \frac{2(170)u}{340}. \] \[ 8=u. \] \[ u=8\,ms^{-1}. \] Therefore \[ \boxed{8\,ms^{-1}}. \]
Was this answer helpful?
0
0
Top TS EAMCET Physics Questions
- A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force $F$ applied perpendicular to the incline. If the mass of the box is $1\,kg$, the angle of inclination is $30^{\circ}$ and the coefficient of static friction between the box and the inclined plane is $0.2$, the minimum magnitude of $\vec{F}$ is (Use $ g = 10\,m/s^2$)
- A metre scale made of steel reads accurately at $25^{\circ} C$ . Suppose in an experiment an accuracy of $0.06\, mm$ in $1\,m$ is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is $ 11 \times 10^{-6} /^{\circ} \, C$ )
- Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will
- A parallel beam of light of intensity \(I_0\) is incident on a coated glass plate. If \(25\%\) of the incident light is reflected from the upper surface and \(50\%\) of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is
- A thermocol box has a total wall area (including the lid) of $1.0 m ^{2}$ and wall thickness of $3 cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is [Use $K_{\text {thermocol }}=0.03 W / mK$ $.L_{\text {fusion (ice) }}=3.00 \times 10^{5} J / kg ]$
View More Questions
Top TS EAMCET Waves Questions
- If the tension applied to a string is decreased by 36\%, then the fundamental frequency of the transverse waves of the string is:
- The frequency of sound heard by a stationary observer is \( f_1 \), when the source of sound is approaching the observer with a speed of 10\% of the speed of sound. If the same source of sound is moving away from the stationary observer with a speed of 20\% of the speed of sound, the frequency of sound heard by the observer is \( f_2 \). Then \( f_1 : f_2 \) is:
- If the tension applied to a string is decreased by 36%, then the fundamental frequency of the transverse waves of the string is:
- The frequency of sound heard by a stationary observer is \( f_1 \), when the source of sound is approaching the observer with a speed of 10% of the speed of sound. If the same source of sound is moving away from the stationary observer with a speed of 20% of the speed of sound, the frequency of sound heard by the observer is \( f_2 \). Then \( f_1 : f_2 \) is:
Wave picture of light has failed to explain
(1) photoelectric effect
(2) interference of light
(3) diffraction of light
(4) polarization of light
View More Questions
Top TS EAMCET Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is
View More Questions