A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of \( 10 m s^{–1}\). What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of \( 10 m s^{–1}\)? The speed of sound in still air can be taken as \( 340 m s^{–1}\)

Asked by Pragya Singh | 1 year ago |  149

1 Answer

Solution :-

Frequency of the whistle = 400 Hz

Speed of wind, vw= 10 m/s

Speed of sound in still air,v= 340 m/s

Effective speed of the sound for an observer standing on the platform

v’ = v + v= 340 + 10 = 350 m/s

There is no relative motion between the source and the observer, therefore the frequency of the sound heard by the observer will be the same.

Therefore, f = 400 Hz

Wavelength of the sound heard by the observer 

\(\dfrac{speed \;of\; wave}{frequency}\)

\( \dfrac{350}{400}\) = 0.875 m

When the air is still and the observer runs towards the yard at a speed of 10 ms–1 then there is a relative motion between the observer the source with respect to the medium.

The medium is at rest. Therefore

v’ = v = 340 m/s

The change in frequency, f ‘ 

=\( \dfrac{(v + v_0)}{v}\times f\)

\( \dfrac{(340 + 10)}{400}\) = 411.76 Hz

Wavelength = \(\dfrac{340}{411.76}\) =  0.826  m

Obviously, the situations in the two cases are entirely different.

Answered by Abhisek | 1 year ago

Related Questions

A truck parked outside a petrol pump blows a horn of frequency 200 Hz in still air.  The Wind then starts blowing towards the petrol pump at 20 m/s. Calculate the wavelength, speed, and frequency of the horn’s sound for a man standing at the petrol pump. Is this situation completely identical to a situation when the observer moves towards the truck at 20 m/s and the air is still?

Class 11 Physics Waves View Answer

A man standing at a certain distance from an observer blows a horn of frequency 200 Hz in still air.

(a) Find the horn’s frequency for the observer when the man

(i) runs towards him at 20 m/s 

(ii) runs away from him at 20 m/s.
 

(b) Find the speed of sound in both the cases. [Speed of sound in still air is 340 m/s]

Class 11 Physics Waves View Answer

A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in the air. What frequency does the bat hear reflected off the wall?

Class 11 Physics Waves View Answer

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of the S wave is about \( 4.0 km s^{–1}\), and that of the P wave is \( 8.0 km s^{–1}.\) A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in a straight line, at what distance does the earthquake occur?

Class 11 Physics Waves View Answer

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of \( 360 km h^{–1}\). What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be \( 1450 m s^{–1}\) .

Class 11 Physics Waves View Answer