Advertisements
Advertisements
Question
An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = 324 m s−1
Advertisements
Solution
Given:
Velocity of sound in air v = 324 ms−1
Frequency of sound sent by source \[n_0\]= 400 Hz
Let the speed of the car be x m/s.
The frequency of sound heard at the car n is given by :
\[n = \frac{v + v_{car}}{v} \times n_0 \]
\[ \Rightarrow n = \frac{324 + x}{324} \times 400 . . . . . \left( 1 \right)\]
If \[n_1\] is the frequency of sound heard by the operator, then its value is given by :
\[n_1 = \frac{324}{324 - x} \times n\]
\[410 = \frac{324}{324 - x} \times n\]
On substituting the value of n from equation (1), we have :
\[410 = \frac{324}{\left( 324 - x \right)} \times \frac{\left( 324 + x \right)}{324} \times 400\]
\[ \Rightarrow 410 = \left( \frac{324 + x}{324 - x} \right) \times 400\]
\[ \Rightarrow 410 \left( 324 - x \right) = 400\left( 324 + x \right)\]
\[ \Rightarrow 324 \left( 410 - 400 \right) = 810x\]
\[ \Rightarrow x = 4 \text{ m/s }\]
The speed of the car is 4 m/s.
APPEARS IN
RELATED QUESTIONS
Which of the following is a mechanical wave?
Both the strings, shown in figure, are made of same material and have same cross section. The pulleys are light. The wave speed of a transverse wave in the string AB is
\[\nu_1\] and in CD it is \[\nu_2\]. Then \[\nu_1 / \nu_2\]
Two particles A and B have a phase difference of π when a sine wave passes through the region.
(a) A oscillates at half the frequency of B.
(b) A and B move in opposite directions.
(c) A and B must be separated by half of the wavelength.
(d) The displacements at A and B have equal magnitudes.
In a stationary wave,
(a) all the particles of the medium vibrate in phase
(b) all the antinodes vibrates in phase
(c) the alternate antinodes vibrate in phase
(d) all the particles between consecutive nodes vibrate in phase.
At a prayer meeting, the disciples sing JAI-RAM JAI-RAM. The sound amplified by a loudspeaker comes back after reflection from a building at a distance of 80 m from the meeting. What maximum time interval can be kept between one JAI-RAM and the next JAI-RAM so that the echo does not disturb a listener sitting in the meeting. Speed of sound in air is 320 m s−1.
In Quincke's experiment the sound detected is changed from a maximum to a minimum when the sliding tube is moved through a distance of 2.50 cm. Find the frequency of sound if the speed of sound in air is 340 m s−1.
In a resonance column experiment, a tuning fork of frequency 400 Hz is used. The first resonance is observed when the air column has a length of 20.0 cm and the second resonance is observed when the air column has a length of 62.0 cm. (a) Find the speed of sound in air. (b) How much distance above the open end does the pressure node form?
Two successive resonance frequencies in an open organ pipe are 1944 Hz and 2592 Hz. Find the length of the tube. The speed of sound in air is 324 ms−1.
Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 cm and the other of 32.2 cm. The speed of sound in air is 350 m s−1.
A tuning fork of unknown frequency makes 5 beats per second with another tuning fork which can cause a closed organ pipe of length 40 cm to vibrate in its fundamental mode. The beat frequency decreases when the first tuning fork is slightly loaded with wax. Find its original frequency. The speed of sound in air is 320 m s−1.
A bat emitting an ultrasonic wave of frequency 4.5 × 104 Hz flies at a speed of 6 m s−1between two parallel walls. Find the fractional heard by the bat and the beat frequencies heard by the bat and the beat frequency between the two. The speed of sound is 330 m s−1.
A bullet passes past a person at a speed of 220 m s−1. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. Speed of sound in air = 330 m s−1.
A violin player riding on a slow train plays a 440 Hz note. Another violin player standing near the track plays the same note. When the two are closed by and the train approaches the person on the ground, he hears 4.0 beats per second. The speed of sound in air = 340 m s−1. (a) Calculate the speed of the train. (b) What beat frequency is heard by the player in the train?
Figure shows a person standing somewhere in between two identical tuning forks. each vibrating at 512 Hz. If both the tuning forks move towards right a speed of 5.5 m s−1, find the number of beats heard by the listener. Speed of sound in air = 330 m s−1.
Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of 36 km h−1 and the other at 54 km h−1 relative to the water. The first submarine sends a sound signal (sound waves in water are also called sonar) at a frequency of 2000 Hz. (a) At what frequency is this signal received from the second submarine. At what frequency is this signal received by the first submarine. Take the speed of of the sound wave in water to be 1500 m s−1.
The speed of sound in hydrogen is 1270 m/s. The speed of sound in the mixture of oxygen and hydrogen in which they are mixed in 1:4 ratio is
Change in temperature of the medium changes ______.
