A siren emitting a sound of frequency $800\, Hz$ moves away from an observer towards a cliff at a speed of $15\,m\,s^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is :
(Take velocity of sound in air = $330 \, ms^{-1}$)
- 800 Hz
- 838 Hz
- 885 Hz
- 765 Hz
The Correct Option is B
Solution and Explanation
Frequency Calculation Using Doppler Effect
The correct option is (B): 838 Hz.
Step-by-Step Calculation:
The formula used to calculate the observed frequency \(n'\) when the source of sound is moving is given by:
\(n' = \frac{v}{v - v_s} n_0\)
Where: - \( v \) is the speed of sound (330 m/s), - \( v_s \) is the speed of the source (15 m/s), - \( n_0 \) is the emitted frequency (800 Hz).
Substituting the given values into the formula:
\(n' = \frac{330}{330 - 15} (800) = \frac{330 \times 800}{315} = 838 \, \text{Hz}\)
Conclusion:
The observed frequency \(n'\) is 838 Hz.
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave