Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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?
Can you hear your own words if you are standing in a perfect vacuum? Can you hear your friend in the same conditions?
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.
Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be P1 and that by the second wave be P2. Then
A small source of sounds moves on a circle as shown in figure and an observer is sitting at O. Let \[v_1, v_2, v_3\] be the frequencies heard when the source is at A, B and C respectively.
A source of sound moves towards an observer.
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 steel tube of length 1.00 m is struck at one end. A person with his ear closed to the other end hears the sound of the blow twice, one travelling through the body of the tube and the other through the air in the tube. Find the time gap between the two hearings. Use the table in the text for speeds of sound in various substances.
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.
The absolute temperature of air in a region linearly increases from T1 to T2 in a space of width d. Find the time taken by a sound wave to go through the region in terms of T1, T2, d and the speed v of sound at 273 K. Evaluate this time for T1 = 280 K, T2 = 310 K, d = 33 m and v = 330 m s−1.
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.
A source S and a detector D are placed at a distance d apart. A big cardboard is placed at a distance \[\sqrt{2}d\] from the source and the detector as shown in figure. The source emits a wave of wavelength = d/2 which is received by the detector after reflection from the cardboard. It is found to be in phase with the direct wave received from the source. By what minimum distance should the cardboard be shifted away so that the reflected wave becomes out of phase with the direct wave?
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.
In a standing wave pattern in a vibrating air column, nodes are formed at a distance of 4.0 cm. If the speed of sound in air is 328 m s−1, what is the frequency of the source?
A tuning fork of frequency 256 Hz produces 4 beats per second with a wire of length 25 cm vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire we shortened so that it produces no beats with the tuning fork?
For the propagation of longitudinal waves, the medium must have
- elasticity
- mass
- inertia
- force of cohesion
During propagation of a plane progressive mechanical wave ______.
- all the particles are vibrating in the same phase.
- amplitude of all the particles is equal.
- particles of the medium executes S.H.M.
- wave velocity depends upon the nature of the medium.
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms-1. The third resonance is observed when the air column has a length of ______ cm.
