Advertisements
Advertisements
Question
Two electric trains run at the same speed of 72 km h−1 along the same track and in the same direction with separation of 2.4 km between them. The two trains simultaneously sound brief whistles. A person is situated at a perpendicular distance of 500 m from the track and is equidistant from the two trains at the instant of the whistling. If both the whistles were at 500 Hz and the speed of sound in air is 340 m s−1, find the frequencies heard by the person.
Advertisements
Solution
Given:
Speed of sound in air v = 340 ms−1
Frequency of whistles \[f_0\]= 500 Hz
Speed of train \[v_s\]= 72 km/h =\[72 \times \frac{5}{18} = 20 \text { m/s }\]
The person will receive the sound in a direction that makes an angle θ with the track. The angle θ is given by :
\[\theta = \tan^{- 1} \left( \frac{0 . 5}{2 . 4/2} \right) = 22 . 62^\circ\]
The velocity of the source will be 'v cos θ' when heard by the observer.
So, the apparent frequency received by the man from train A is
\[f_1 = \left( \frac{v}{v - v_s \cos\theta} \right) \times f_0 \]
\[ \Rightarrow f_1 = \left( \frac{340}{340 - v_s \cos 22 . {62}^\circ} \right) \times 500\]
\[ \Rightarrow f_1 = \left( \frac{340}{340 - 20 \times \cos 22 . 62^\circ} \right) \times 500\]
\[ \Rightarrow f_1 = 528 . 70 \text{ Hz } \approx 529 \text { Hz }\]
The apparent frequency heard by the man from train B is
\[f_2 = \left( \frac{v}{v + v\cos\theta} \right) \times f_0 \]
\[ \Rightarrow f_2 = \left( \frac{340}{340 + 20 \times \cos 22 . 62^\circ} \right) \times 500\]
\[ \Rightarrow f_2 = 474 . 24 \text { Hz } \approx 474 \text { Hz }\]
APPEARS IN
RELATED QUESTIONS
Explain what is Doppler effect in sound
A wave is represented by an equation \[y = c_1 \sin \left( c_2 x + c_3 t \right)\] In which direction is the wave going? Assume that \[c_1 , c_2\] \[c_3\] are all positive.
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?
If you are walking on the moon, can you hear the sound of stones cracking behind you? Can you hear the sound of your own footsteps?
When we clap our hands, the sound produced is best described by Here p denotes the change in pressure from the equilibrium value.
A tuning fork sends sound waves in air. If the temperature of the air increases, which of the following parameters will change?
A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is
When you speak to your friend, which of the following parameters have a unique value in the sound produced?
Ultrasonic waves of frequency 4.5 MHz are used to detect tumour in soft tissue. The speed of sound in tissue is 1.5 km s−1 and that in air is 340 m s−1. Find the wavelength of this ultrasonic wave in air and in tissue.
A sources of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all directions. The speed of sound in air is 340 m s−1 and the density of air is 1.2 kg m −3. (a) What is the intensity at a distance of 6.0 m from the source? (b) What will be the pressure amplitude at this point? (c) What will be the displacement amplitude at this point?
A source of sound S and detector D are placed at some distance from one another. a big cardboard is placed near hte detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is 336 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?
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.
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.
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?
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 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.
A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of 72 km h−1. The signal travelling at 330 m s−1 in air and having a frequency of 1600 Hz gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person.
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.
