Advertisements
Advertisements
Question
A train running at 108 km h−1 towards east whistles at a dominant frequency of 500 Hz. Speed of sound in air is 340 m/s. What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the track hear whom the train has just passed? (c) A wind starts blowing towards east at a speed of 36 km h−1. Calculate the frequencies heard by the passenger in the train and by the person standing near the track.
Advertisements
Solution
Given:
Velocity of sound in air v = 340 m/s
Velocity of source vs = 108 `\text{ kmh}^\(-)`1 =\[\frac{108 \times 1000}{60 \times 60} = 30 {\text { ms }}^{- 1}\]
Frequency of the source \[n_0\]= 500 Hz
(a) Since the velocity of the passenger with respect to the train is zero, he will hear at a frequency of 500 Hz.
(b) Since the observer is moving away from the source while the source is at rest:
Velocity of observer \[v_o\]= 0
Frequency of sound heard by person standing near the track is given by:
\[n = \left( \frac{v}{v + v_s} \right) n_0 \]
Substituting the values, we get:
\[n = \frac{340}{340 + 30} \times 500 = 459 \text{ Hz }\]
(c) When medium (wind) starts blowing towards the east:
Velocity of medium vm = 36 `\text { kmh}^\(-)`1 =\[36 \times \frac{5}{18} = 10 {\text { ms }}^{- 1}\]
However, frequency heard by person standing near the track is given by:
\[n = \frac{\left( v + v_m \right)}{\left( v + v_m \right) + v_s} \times n_0 \]
\[ = \frac{\left( 340 + 10 \right)}{\left( 340 + 10 \right) + 30} \times 500\]
\[ = 458 \text{ Hz }\]
APPEARS IN
RELATED QUESTIONS
Explain what is Doppler effect in sound
A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?
The voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
A listener is at rest with respect to the source of sound. A wind starts blowing along the line joining the source and the observer. Which of the following quantities do not change?
(a) Frequency
(b) Velocity of sound
(c) Wavelength
(d) Time period
A man stands before a large wall at a distance of 50.0 m and claps his hands at regular intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value when the echo of a clap merges every 3 seconds, find the velocity of sound in air.
A person can hear sound waves in the frequency range 20 Hz to 20 kHz. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is 360 m s−1.
The equation of a travelling sound wave is y = 6.0 sin (600 t − 1.8 x) where y is measured in 10−5 m, t in second and x in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.
The length of the wire shown in figure between the pulley is 1⋅5 m and its mass is 12⋅0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.
Sound with intensity larger than 120 dB appears pain full to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?
A string of length L fixed at both ends vibrates in its fundamental mode at a frequency ν and a maximum amplitude A. (a)
- Find the wavelength and the wave number k.
- Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.
The two sources of sound, S1 and S2, emitting waves of equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to S1 S2 and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in detector should be shifted to detect a minimum of sound.
Three sources of sound S1, S2 and S3 of equal intensity are placed in a straight line with S1S2 = S2S3. At a point P, far away from the sources, the wave coming from S2 is 120° ahead in phase of that from S1. Also, the wave coming from S3 is 120° ahead of that from S2. What would be the resultant intensity of sound at P?
Two coherent narrow slits emitting sound of wavelength λ in the same phase are placed parallel to each other at a small separation of 2λ. The sound is detected by moving a detector on the screen ∑ at a distance D(>>λ) from the slit S1 as shown in figure. Find the distance x such that the intensity at P is equal to the intensity at O.
Figure shown two coherent sources S1 and S2 which emit sound of wavelength λ in phase. The separation between the sources is 3λ. A circular wire of large radius is placed in such way that S1,S2 is at the centre of the wire. Find the angular positions θ on the wire for which constructive interference takes place.
Show that if the room temperature changes by a small amount from T to T + ∆T, the fundamental frequency of an organ pipe changes from v to v + ∆v, where \[\frac{∆ v}{v} = \frac{1}{2}\frac{∆ T}{T} .\]
A cylindrical tube, open at both ends, has a fundamental frequency v. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is
A traffic policeman standing on a road sounds a whistle emitting the main frequency of 2.00 kHz. What could be the apparent frequency heard by a scooter-driver approaching the policeman at a speed of 36.0 km h−1? Speed of sound in air = 340 m s−1.
A sound source, fixed at the origin, is continuously emitting sound at a frequency of 660 Hz. The sound travels in air at a speed of 330 m s−1. A listener is moving along the lien x= 336 m at a constant speed of 26 m s−1. Find the frequency of the sound as observed by the listener when he is (a) at y = − 140 m, (b) at y = 0 and (c) at y = 140 m.
